Lorentz-HA: Arbiter (Step 3)

Revised after QE (2026-10-08): see "QE revision" below. No final verdict reverses. Claim 8 is added, and the wording of claims 2, 3, 4 and 7 is tightened.

Project: H. A. Lorentz, The Theory of Electrons and its Applications to the Phenomena of Light and Radiant Heat (2nd ed., Teubner 1916; Columbia lectures March-April 1906; text of 1909 with [1915] notes). Date 2026-10-08.

Tags: [read] = the book (PDF page; printed page = PDF page minus 9), [read: page image p.N] = rendered page, [web] with URL, [memory] with confidence, [calc] = recomputed by the arbiter.

Source gap: none. The OCR text is readable, and Chapter V (PDF pp.196-239) and Notes 72, 75, 86 were read from page images in the deep read. Chapters I-IV and Notes 1-61 rest on digests only; only claim 7 touches them, and nothing in the verdicts below depends on it. No conclusion rests on [memory] alone, except the items marked so in "Web checks".

How I worked

I read physicist.md, mathematician.md, contrarian.md, claims.md, facts.json, sites.md and the research notes once. I rendered PDF p.228 myself (200 dpi) to settle the one factual disagreement between reviewers (Brace, below). I re-did the numbers that differed. I used 2 web calls (budget 8) and grepped the Investigator's saved Wikipedia text for the electron-mass experiments.

Where the reviewers differ on facts, and my recomputation

1. Brace's reach: 10^-12 or 10^-13? The physicist and the contrarian read 10^-12 from the page image; the mathematician says the text gives "1e-13" and calls the "twentieth part" an inconsistency in Lorentz. I rendered p.228. The printed figure is 10^-12 ("a difference between the principal refractive indices of 10^-12 could not have escaped him. This is about the twentieth part of the value which we have just computed") [read: page image p.228]. [calc] 2e-11 / 1e-12 = 20, which is the "twentieth part"; there is no slip by Lorentz. The mathematician's reading came from the garbled text layer (and from claims.md and facts.json, which carry 1e-13). Physicist and contrarian are right; the mathematician's Correction 3 is withdrawn. The margin on the rigid sphere is a factor of about 20, not 200.
2. Brace's own figures [web]. Brace's 1904 paper (Wikisource copy) states a sensitivity of about 7.8e-13 in index difference (about 6e-5 of a wavelength), against a largest expected effect of about 5e-9 in his own calculation, "about 1600 times greater than the smallest effect which could be observed" [web: https://en.wikisource.org/wiki/On_Double_Refraction_in_Matter_moving_through_the_Aether; the fetch returned a model summary of the page, not the whole text]. Two readings that should not be mixed: Lorentz's 2e-11 is a different calculation from Brace's 5e-9 (Lorentz says so: "Brace himself has made the calculation in a different manner" [read: page image p.228]), and 1e-12 (Lorentz) versus 7.8e-13 (Brace) are the same order. Brace's own number for the first-order-in-beta^2 contraction effect with the dispersion not considered is much larger, which is why Brace first read his null as a refutation of contraction [web: research/wiki-Experiments_of_Rayleigh_and_Brace.txt]. The verdict on claim 4 does not change: with the corrected margin the exclusion of the rigid sphere is about 20 (Lorentz's computation) and depends on his assumption that the electron mass enters the optics through m n^2.
3. Constant-volume electron. The mathematician says Lorentz gives 2e-11 only for the rigid sphere and "even a little stronger" for the constant-volume electron [read: page image p.229]. The contrarian and claims.md say both predict about 2e-11. I accept the mathematician's wording: "at least about 2e-11 for the rigid sphere; a little stronger for the constant-volume electron". I did not re-read p.229.
4. Michelson-Morley was an upper bound, not an exact zero. The contrarian's point stands. 1887: at most 0.02 fringe against 0.40 expected, which is 1/20, not 1/40 (QE: Wikipedia says "as small as one-fortieth"; the 1887 paper says "certainly less than the twentieth part ... probably less than the fortieth part" [memory, high]) [web: https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment, checked now]. 1905 Morley-Miller: less than one-hundredth [read: p.204]. [calc] 22 m x 1e-8 / 589 nm = 0.37 fringe, so Lorentz's 0.4 is right.
5. Reciprocity needs l = 1 (mathematician). [calc by reasoning, not re-run by me]: with an even scale factor l(w), the transformation with w replaced by -w composed with the forward one gives l^2 times the identity, so the pair is an exact inverse only if l = 1. Physicist and contrarian agree l = 1 is fixed only through the mass assumptions (Note 75*, p.337ff). Accepted.
6. "Wholly electromagnetic" mass. The mathematician's point: including the Poincare stress, the rest energy m0 c^2 = e^2/(6 pi R) is 4/3 of the field's own energy e^2/(8 pi R) [calc: (1/6)/(1/8) = 4/3]. The momentum is entirely field momentum; a quarter of the rest energy is stress energy. Accepted; the physicist's modern view (stress needed to get a four-vector) agrees.
7. 1909 Note 87. All three accept the Investigator: the first edition already said Bucherer (1908) confirmed (313); 1915 widened the list [web: archive.org cu31924005244615 via research/2026-10-08-internet-archive.md; not re-fetched by me]. Lorentz's reversal on the deformable electron therefore rests, in 1909, on one experiment.

Corrected claim list

Page numbers are PDF pages. Verdicts use the Step 2 scale.

Claim 1. The exact transformation x' = kl(x - wt), t' = kl(t - wx/c^2) leaves the free-ether Maxwell equations of form; l = 1 is the Lorentz transformation

Corrected statement: Lorentz gives the transformation with a scale factor l; the free-ether equations are invariant for any l [calc by mathematician and physicist]. l = 1 is not derived from the field equations; it is forced by the mass assumptions (Note 75). With charges and currents, the 1906/1909 version is not exactly form-invariant, because his auxiliary velocity and density (289)-(290) are not the relativistic ones (factor (1 - w u'_x/c^2) in (292)); he says so on p.239 and in Note 72. Voigt (1887) had an equivalent transformation, which Lorentz concedes in a footnote (p.207) [read]; Poincare, Larmor and others contributed before and after [memory, medium; priority is outside the physics verdict]. - Agreement: all three: mathematics consistent, experimentally established, tested by many groups. Difference: only emphasis on the caveats. No real dispute. - What would settle it: nothing outstanding for the transformation itself. - Final verdict: Established (the transformation and invariance of the free-ether equations). Qualifier: Lorentz's own derivation for matter, with general l, was incomplete, as he states.

Claim 2. If molecular and elastic forces transform like electrostatic forces, bodies contract by k, so Michelson-Morley must be null; "with an immovable ether, Michelson's experiment proves the contraction"

Corrected statement: the null result is an upper bound (1887: certainly below 1/20 of the expected 0.40 fringe, i.e. at most 0.02 fringe, and probably below 1/40; 1905: below 1/100), not an exact zero [wording corrected, QE revision (a)]. Trouton-Rankine (1908) looked for an effect of motion on a charged capacitor and found none [web, as reported by the physicist and contrarian: https://en.wikipedia.org/wiki/Trouton%E2%80%93Rankine_experiment; restored by QE revision (d)]. The experiment fixes only the ratio of the two arm lengths (needed: L parallel / L perpendicular = 1/k) and not a cause. Lorentz's "proves" is conditional on an immovable ether and on nothing else compensating (p.205), and on two stated hypotheses: molecular forces obey (300), and equilibrium is unique (pp.210-211). - Agreement: all three accept the arithmetic and that "proves" is too strong. Disagreement on the label for the dynamical derivation: physicist "Plausible, untested"; mathematician "Plausible, untested" for non-electromagnetic forces plus "Not testable as stated" for the cause; contrarian "Not testable as stated". - Which is stronger: the contrarian and mathematician. A dynamical contraction by forces and the kinematic contraction of relativity make identical predictions once all forces are Lorentz-covariant, so there is no measurable difference to test. The physicist's point that the premise (all binding forces covariant) is an extra assumption is right and I keep it, but that premise has been tested indirectly by every later null and precision test, not left untested. Note 75 concedes that distance-only forces do not obey the law [read: p.340]. - What would settle it: nothing within Lorentz-covariant theories. A neutral test needs a Lorentz-violating observable (a preferred-frame signature in a cavity, clock or Ives-Stilwell-type experiment); current bounds are 1e-8 to 1e-17 depending on the observable [web: https://arxiv.org/pdf/1002.1284 (cited by the physicist), https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment]. - Final verdict (split): - Contraction with time dilation as the observable ratio and its consequences: Established. - Contraction as the dynamical effect of absolute motion through an ether, via (300): Not testable as stated (same predictions as special relativity). Its premise for non-electromagnetic forces is an assumption that later tests support only indirectly. - "Michelson's experiment proves the contraction": Historically superseded but instructive* (valid only as a conditional; Kennedy-Thorndike 1932 showed contraction alone was never enough [web: research/wiki-Kennedy-Thorndike_experiment.txt]).

Claim 3. Deformable electron held by a Poincare stress; masses m' = k^3 m0, m'' = k m0; Kaufmann 1906 "decidedly unfavourable"; later experiments "confirm"

Corrected statement (replaces "must"): Lorentz works out a deformable electron as the way to get these masses; he does not say it must be so. He calls the idea "tempting", says Kaufmann's data make it "very likely that we shall have to relinquish this idea altogether", later says it is "quite legitimate to maintain the hypothesis", concedes stability is not shown and that "perhaps ... we are wholly on the wrong track when we apply to the parts of an electron our ordinary notion of force" [read: pp.221-224]. The 1909 first edition already cited Bucherer 1908 as confirming (313); the [1915] Note 86 adds Hupka, Schaefer and Neumann, Guye and Lavanchy [read: p.348; web via Investigator]. The mass is "wholly electromagnetic" only for momentum; energy needs the stress (item 6 above). Added by QE revision (f): in Chapter I (p.51-52) Lorentz himself takes Kaufmann's 1906 data to fit Abraham's rigid sphere and adopts "Kaufmann's conclusion, or hypothesis" that the negative electron has no material mass, a statement left unqualified in the 1915 edition; he adds that a material mass of about 1% of the electromagnetic one cannot be excluded, and drops it "with a view to simplicity". The 1915 footnote to section 179 reads "This can no longer be said now" [read: QE deep read, pp.51-52, 221]. - Agreement: algebra checks (momentum 311, energy 315, Poincare stress, l = 1 from 312-313: SymPy residue 0 by three reviewers' accounts); the relativistic mass law is Established; the shell model is not a modern electron. - Disagreement: the label for the shell (physicist and mathematician "Historically superseded but instructive"; contrarian "Not testable as stated", because it makes no distinct prediction) and for Kaufmann. - Which is stronger: the shell makes more than one claim. The part "mass wholly electromagnetic" has been given up in the book's own terms (Poincare stress, instability) and by modern treatment of the electron as a point particle [memory, high]. The part "no distinct prediction" is the contrarian's, and it is also true: the shell gives the same masses as special relativity. I label the shell historically superseded (a reasonable 1906-09 position, replaced) and note that it is not testable against SR. - Experimental weighing: Kaufmann (1901-06) fit Abraham's rigid sphere; Planck's reanalysis found the data not fully decisive; Bucherer 1908 favoured Lorentz-Einstein (Bestelmeyer disputed the method); Zahn-Spees 1938 and Farago-Janossy 1954/57 argued that these early experiments showed only a qualitative mass increase; Rogers, McReynolds and Rogers (Phys. Rev. 57, 379, 1940) first fit the Lorentz-Einstein curve to within about 1% [web: Wikipedia KBN page, checked against the saved copy research/pages/wiki-kaufmann-bucherer-neumann.txt; DOIs 10.1103/PhysRev.53.511 and 10.1103/PhysRev.57.379; primary papers not read]. Lorentz's 1909/1915 confidence rested on experiments the field later judged less decisive than he thought; the formula nonetheless survived the sharper tests. Both statements stay in the record. - What would settle it: reading Zahn-Spees (1938), Farago-Janossy (1957) and Potters (HSNS 2023, PhilSci-Archive 22988) to quantify how far Bucherer 1908 and Neumann 1914 actually separated Abraham from Lorentz-Einstein; and NHA archive 364 items 501, 135, 486 (Lorentz's own calculations on Kaufmann and Bucherer). [calc by the physicist] the ratio of relativistic to Abraham transverse mass is 1.03 at beta 0.5, 1.08 at 0.7, 1.26 at 0.9, so discrimination needs good data above beta of about 0.8. - Glitscher 1917 (hydrogen fine structure) and Neumann 1914 are later tests of the same law, in the mathematician's and contrarian's files; restored by QE revision (d) [web: https://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments, as reported]. - Final verdict (split): - Mass-velocity law m' = k^3 m0, m'' = k m0 (momentum k m0 v): Established (decisive tests from 1940 and accelerator physics, after Lorentz). - Deformable shell with Poincare stress as the physical electron, mass wholly electromagnetic: Historically superseded but instructive; Lorentz's 1909 acceptance rested on a single, later contested, experiment. - Abraham's rigid sphere (the rival): Tested, not supported. - "The negative electron has no material mass at all" (Chapter I, p.52, adopted from Kaufmann's 1906 conclusion "or hypothesis", with a 1% material mass not excluded): Historically superseded but instructive (added by QE revision (f); it rests on the same early data whose power the arbiter rates below the 1940 tests, and on one common unit charge, which Note 16 of 1915 calls "not wholly elucidated"). - Kaufmann 1906 as an exclusion of the formula: Tested, not supported* at the time as a reading of the data, later reversed; the data's discriminating power was overrated, which is the instructive part.

Claim 4. Rigid (Abraham) and constant-volume electrons predict double refraction of about 2e-11 in water; Brace (reach 10^-12) saw none

Corrected statement (two corrections): Brace's reach as Lorentz states it is 10^-12 (the page image), a factor of 20 below the prediction; the 2e-11 figure is for the rigid sphere, and the constant-volume electron gives an effect "even a little stronger". Frequency change (1/10) beta^2 n = 1e-9 n at beta = 1e-4 [read: page image p.228]; [calc] the index change with water's dispersion gives about 2.0e-11 (my check: n about 1.3371 at 486 nm and 1.3312 at 656 nm [memory, medium], lambda x |dn/dlambda| about 0.020; the physicist and mathematician got 2.0e-11 and 1.8e-11, same result in order). - Agreement: all three: mathematics consistent; Tested, not supported. Difference: strength of the margin (20, not 200) and its model dependence (Lorentz's own hedge; the m n^2 assumption). - Brace's paper gives 7.8e-13 as his sensitivity [web, above], consistent in order with Lorentz's 1e-12. No independent replication of Brace is documented in the review files; Rayleigh (1902, 76 cm tube) and Brace (1904, 4.13 m of water, light path 28.5 m [web: wiki Experiments of Rayleigh and Brace]; Brace's own paper says "30 metres of water", QE check 6) are two independent null experiments. Brace also ran glass with precision about 4.5e-11 [web, same page]. - What would settle it: Brace's original paper read in full (his own calculation, which Lorentz says differs) and a modern repetition; neither is needed for the verdict. - Final verdict: Tested, not supported (for the rigid-sphere and constant-volume electron models, within Lorentz's dispersion assumption; margin about 20 for the rigid sphere). The null result does not itself prove the deformable electron.

Claim 5. Moving observer: clocks slow by k, light speed c, light-signal synchronisation gives local time, descriptions reciprocal

Corrected statement: the result is conditional on the rods and clock-work obeying (300) (p.233), and reciprocity needs l = 1. Both statements "A's clocks go k times slower than A0's" and the reciprocal one are consistent: they compare different sets of events. [calc by physicist and mathematician]: round trip 2cL/(k(c^2 - w^2)) = 2kL/c; the synchronisation reading equals k(t - wx/c^2); the inverse is (330). - Agreement: all three. Experiments: Ives-Stilwell 1938 (about 1% originally) to storage-ring tests at about 2e-8 (Botermann 2014; the physicist cites +/-2.3e-9 in a different test, arXiv 1409.7951), Kennedy-Thorndike, cavity tests [web, as cited by physicist and contrarian]. The contrarian notes Ives himself kept a Lorentz-Larmor interpretation [web: https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment, as reported]. - What would settle it: nothing needed for the observable content. - Final verdict: Established (clock slowing, c, light-signal synchronisation, reciprocity as predictions). The interpretive layer (the ether-frame times are "true") is claim 6.

Claim 6. Lorentz on Einstein: "simply postulates what we have deduced, with some difficulty and not altogether satisfactorily"; an ether of "a certain degree of substantiality"; Note 72* (1915): his failure came from treating t' as only auxiliary

Corrected statement: quotations are in the book as quoted [read: pp.238-239, 330]. Lorentz's "deduced" depends on hypotheses (300), (305) and l = 1, which are Lorentz covariance of all forces in disguise (Note 75: "relativity requires a general law of force"); the deduction is therefore not independent of the postulate, and Lorentz concedes Einstein's theory "has another marked advantage" (p.239). The same page says no experiment decides which observer moves relative to the ether (p.238). Later statements, recorded as reported by the Investigator: 1913 Das Relativitaetsprinzip ("to a certain degree a dispute about words"; "a certain satisfaction" in an ether with some substantiality and absolute simultaneity) [web: archive.org bub_gb_89PPAAAAMAAJ, not re-read by any reviewer or by me]; the 1927 Mount Wilson remark "I considered my time transformation only as a heuristic working hypothesis. So the theory of relativity is really solely Einstein's work" [web via Wikipedia, ApJ 68 (1928) 341; primary not read; wording unchecked]. Einstein's 1920 Leiden address says the Lorentz ether kept only immobility [web: https://en.wikisource.org/wiki/Ether_and_the_Theory_of_Relativity]; Einstein is an interested party in the priority and interpretation dispute. - Agreement: all three; verdicts match in substance (historical self-assessment superseded; ether preference not testable; modified variants never properly tested). - Disagreement: none of substance. The neo-Lorentzian literature (Bell, Janossy, Prokhovnik, Ives, Robertson-Mansouri-Sexl, Schmelzer, Arminjon, Clube) is empirically equivalent to SR where it keeps the full transformation; the mainstream's label "unfounded" is a Wikipedia characterisation, not a test result. Bischoff van Heemskerck (F1000Research 12:407, 2023), which drops reciprocity and proposes a modified Ives-Stilwell test [web: https://pmc.ncbi.nlm.nih.gov/articles/PMC11318248/; only the abstract was read by reviewers], is an untested, published proposal. - What would settle it: a measured preferred-frame effect (current bounds 1e-8 to 1e-17); for the narrower question of Lorentz's own view, the NHA archive 364 treatise on the ether (item 398), the Einstein letters 1909-1927, and the ADS scan of Lorentz's 1927 remarks (pp.345-351). - Final verdict (split): - Lorentz's historical self-assessment (Einstein postulates what he deduced; t' was the physical time): Historically superseded but instructive. - An ether frame whose rods and clocks are the "natural" standard though no experiment can reveal it: Not testable as stated. - Variants that give up reciprocity and predict different results: Never properly tested* (not dismissed untested; new and unchecked; the standard tests constrain them).

Claim 7 (background). Electron theory reproduces the Zeeman effect, Lorentz-Lorenz refractivity, dispersion, Faraday rotation and the long-wave black-body law

All three rest on digests of Chapters I-IV and Notes 1-61, and say so; none re-derived these. The mathematician did not check the mathematics. Zeeman's 1914-15 repeat of Fizeau's flowing-water experiment agrees with the dispersion-corrected calculation: 0.826 +/- 0.007 observed at 4500 A against 0.825 calculated with the dispersion term and 0.786 without it [read: page image p.329; QE deep read, which replaced the earlier digest-only figure]. See QE revision (f) for the full table and its caveats. - Added by QE revision (g): Chapter II §§58-76 and Notes 38-42 and Chapter V §§146-165 and Notes 65-69 now rest on deep reads, not digests alone (Fresnel drag from the electron model; the long-wave law (148) as the Rayleigh limit of Planck; Jeans's difficulty and the silver-in-the-dark argument). They support the verdicts below. - Final verdict: Established for the normal Zeeman triplet, the Lorentz-Lorenz law, classical dispersion and the Rayleigh-Jeans long-wave limit; Historically superseded but instructive for the classical-oscillator atomic model, the anomalous Zeeman patterns (spin and quantum theory needed) and the short-wave black-body law (Jeans's difficulty; Planck, Note 42*). - What would settle it: a deep read of the rest of Chapters I-IV (Zeeman effect, Lorentz-Lorenz law, Faraday rotation) if a verdict ever depends on them.

Claim 8 (added by QE revision). Stokes's dragged ether (and Planck's condensed ether) as an alternative to Fresnel's stationary ether

See QE revision (h). Final verdict (split): Stokes's incompressible, irrotational, no-slip ether: Internally inconsistent (Lorentz's Note 66, recomputed). Planck-Lorentz condensed ether: Plausible, untested as a mathematical model, with the physical assumptions unreviewed by the three reviewers (provisional; see QE revision (h)).

Corrections to earlier documents

(The orchestrator applies these.) 1. Brace's reach is 10^-12, not 10^-13. Documents: claims.md claim 4; facts.json (Ch. V second part: summary "1e-13 vs 2e-11" and key claim 5); deep/The-theory-of-electrons-and-its-applicat-HA-LORENTZ-d80e55.md (section 7 and reader summary item 3). Evidence: p.228 page image, rendered by the physicist, the contrarian and the arbiter: "10^-12 ... about the twentieth part of the value which we have just computed" (2e-11/1e-12 = 20). The text layer drops the superscript. The mathematician's reading ("1e-13 is 1/200, so Lorentz slipped") is also wrong and is withdrawn. Search every file for "10^-13", "1e-13", "10⁻¹³". Brace's own paper gives 7.8e-13 [web], which is a different statement and should not be substituted for Lorentz's number. 2. claims.md claim 4: "both predict about 2e-11" should read: about 2e-11 for the rigid sphere; "even a little stronger" for the constant-volume electron [read: page image p.229, per the mathematician]. 3. claims.md claim 3: "The electron must be a deformable shell" overstates; use the corrected statement above. Also: Lorentz's reversal dates from the 1909 first edition (Note 87, Bucherer 1908); the [1915] Note 86 widened it. facts.json (Notes 62-86 entry and Ch. V key claim 9) should add this. 4. claims.md claim 2: "null" should say "null within 1/20 certainly, probably 1/40 (1887), and 1/100 (1905), of the expected shift" (wording revised by QE; 0.02 of 0.40 is 1/20). Also add that "proves" is Lorentz's conditional wording. 5. claims.md claim 1 should add: l = 1 is fixed only through the electron mass assumptions; with sources the 1909 equations are not exactly form-invariant (Lorentz says so, p.239 and Note 72); reciprocity needs l = 1. 6. claims.md claim 3 / facts.json "wholly electromagnetic": true for the momentum only; with the Poincare stress, a quarter of the rest energy is stress energy. 7. Earlier digest errors listed in claims.md (m', m'' at p.221; "10^-8 n" should be (1/10) beta^2 n = 1e-9 n; iota is l; eq. 297 has no 4 pi): confirmed by the page images; nothing further. 8. Section-number note (two "176" in the text layer):* accepted from the physicist; not rechecked.

Absence-of-evidence analysis

Lorentz was a Nobel laureate (1902) in a public, well-documented career, so there is no hidden company or lost device here. The record still goes quiet in four places, and each is an anomaly to set out, not a neutral gap.

1. The 1906-1909 change of mind on the deformable electron. In 1906 Lorentz wrote that Kaufmann's data were "decidedly unfavourable" and that the idea should probably be given up [read: p.222]. By 1909 (Note 87) he says Bucherer 1908 removed "the only objection". The book does not record what he learned or computed in between. Competing explanations: (a) he found Bucherer's result convincing on its own merits (his archive holds a note on Bucherer 1908-09, item 135, and letters from Bucherer 1908-09); (b) he had by then Planck's reanalysis of Kaufmann and doubts about Kaufmann's method [web: Wikipedia KBN page, as reported]; (c) the principle of relativity (Einstein 1905, Minkowski 1908) gave him reasons to want the formula to hold [memory, medium]. Evidence for (a) and (b) is on record, for (c) not in the review files. Against: later reviewers (Zahn-Spees, Farago-Janossy) judged Bucherer's data inconclusive, so (a) would mean he acted on a weaker result than he believed. What would decide it: NHA archive 364 items 135, 486, 501 and the Bucherer and Kaufmann letters (Kox's correspondence volumes), and his Leiden lecture notes. Not read by anyone.
2. Where Lorentz stopped publishing on the ether. The book keeps a "substantiality" of the ether in 1909 and the 1913 lectures call the dispute "partly one about words"; the 1915 notes concede t' was the real time. Item 398 of the archive is a treatise defending the concept of the ether, undated, and its date and content are not known. Competing explanations: unfinished draft that he abandoned; a text for lectures; a reply to Einstein's papers. Evidence for any: none in the review files. What would decide it: reading item 398 and dating it, and the 1909-1927 Einstein letters.
3. Voigt 1887 "escaped my notice all these years". Lorentz says this in a footnote (p.207) [read]. The NHA archive holds letters from Voigt from 1888 with a Lorentz draft. The footnote is single-source evidence (Lorentz's own statement) and it is not contradicted anywhere in the files. Explanations: simple oversight (his statement); or knowledge of the paper earlier. Evidence for the second: none found. What would decide it: the 1888 letters.
4. Dayton Miller's non-null drift. Miller reported a small positive drift (about 10 km/s vs about 30 km/s expected), Lorentz corresponded with him in 1906, 1921, 1926 and lectured on his repetitions in 1925-26 (item 289). No one replicated it and a reanalysis (Roberts 2006) found his signals statistically insignificant [web: https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment, as reported]. The line goes dark because the result was set aside, not suppressed: no blocked publication or funding is documented in the review files. What would decide it: Miller's original data and Roberts's analysis, and Shankland 1955 (cited, not read here).

No suppression story is documented for this project. The Investigator found no funding or publication blockage; that is silence in the sources searched, not proof that none occurred.

What would settle it (collected)

• Claim 3, quality of the early electron-mass tests: read Zahn-Spees (Phys. Rev. 53, 511) and Farago-Janossy (Nuovo Cimento 5, 1957) and Potters 2023; compute from Bucherer's own runs how well they separated k^3/k m0 from Abraham's formula (the physicist's ratios, 1.03 at beta 0.5 to 1.26 at 0.9, give the scale).
• Claim 4, Brace: read Brace 1904 in full (Phil. Mag. 7, 317) for his own calculation; check Lorentz's dispersion step (m n^2).
• Claim 6: 1927 Mount Wilson wording (ADS scan pp.345-351), the 1913 text, NHA 364 items 398, 495, 501, 135, 486, Einstein letters.
• Preferred-frame tests: a measured Lorentz-violation signal in resonator, clock or Ives-Stilwell-type tests would separate the neo-Lorentzian ether from SR; Bischoff van Heemskerck's modified Ives-Stilwell test is the one concrete proposal found.

Open questions

1. How good was the 1908-1915 evidence for the relativistic mass law, quantitatively, and why did Lorentz accept it in 1909 on Bucherer alone?
2. Answered by QE revision (b). What did Lorentz write about Poincare's 1905-06 work in this book? He credits Poincare only for the electron's stress and stability (pp.222-224), Voigt for the transformation (p.207), Einstein for the interpretation (sections 189-194); Larmor appears only in the 1909 preface as one of the authors "not mentioned" [read: grep of the text layer, QE]. Why he wrote it this way is not stated in the book.
3. Does any test separate a physical ether frame from SR? No data now; only proposals.
4. What is Brace's exact calculation, and is the factor 20 robust to changing the mass-to-index assumption?
5. When was the ether treatise (NHA item 398) written and what does it argue?
6. Stability of the deformable electron: Lorentz concedes it is not shown; in modern treatment the stress question is subsumed by treating the electron as pointlike with a mass parameter [memory, high].

Web checks (budget 8, used 2; QE added 2 of its own, see QE revision) and unchecked [memory] items

• Brace's sensitivity and expected effect: checked [web: https://en.wikisource.org/wiki/On_Double_Refraction_in_Matter_moving_through_the_Aether] (7.8e-13; a model summary of the page).
• Michelson-Morley 1887 (one-fortieth; 0.02 vs 0.40), Miller (about 10 km/s), Roberts 2006, modern 1e-17: checked [web: https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment]. Shankland 1955 not opened.
• Rogers 1940 and Zahn-Spees 1938 (as reported on the Wikipedia KBN page; citations only, papers unread).
• Not checked, no verdict depends on them: electron classical radius 2.8e-15 m versus point-like to below about 1e-18 m [memory, medium]; Poincare's and Larmor's priority [memory, medium]; Nobel 1902 [memory, high]; the 1927 Mount Wilson wording [web via Wikipedia, unread primary]; water's dispersion values [memory, medium; the magnitude check agrees with Lorentz's 2e-11].

Summary of final verdicts

QE revision (2026-10-08)

Arbiter, after reading qe.md (verdict MINOR) and the four new deep reads appended to deep/The-theory-of-electrons-and-its-applicat-HA-LORENTZ-d80e55.md: Notes 69/69 (Zeeman and Michelson-Morley), Chapter I §§26-36 with section 179 and Notes 16, 17 and 86, Chapter II §§58-76 with Notes 38-42*, and Chapter V §§146-165 with Notes 65-68. I read all four in full, and QE's own page-image checks are taken from qe.md. Tags as above. Web budget: the arbiter used 2 of 8 before; this revision ran no new web call (see "Not done" at the end).

Result: no final verdict on claims 1-7 reverses. What changes: (1) wording of claims 2, 3, 4 and 7 (edited above in place); (2) claim 3 gets one more line in its split verdict ("no material mass"); (3) claim 7 now rests partly on deep reads, and its Zeeman figure is verified; (4) a claim 8 is added (the dragged-ether alternative, which no review file weighed); (5) open question 2 is answered. The edits are tagged "QE revision" in the text above so the earlier wording can be compared.

(a) Michelson-Morley 1887 bound (QE check 7)

The arbiter wrote "about one-fortieth (0.02 fringe against 0.40 expected)". The two numbers give 0.02/0.40 = 1/20 [calc]. Wikipedia says the measurement was "as small as one-fortieth"; the 1887 paper's wording is "certainly less than the twentieth part ... and probably less than the fortieth part" [memory, high; wording not re-fetched; https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment for the Wikipedia statement]. Corrected form: certainly below 1/20 (at most 0.02 of the 0.40 fringe expected), probably below 1/40. The Lorentz 22 m / 0.4 fringe arithmetic stands (QE check 3, page image p.204). Claim 2's verdict is unchanged. The same fix is needed in contrarian.md (Correction 3) and primer.md §3.2 and evidence-table row 2.

(b) Open question 2, answered from the book (QE section 3, item 2)

QE searched the text layer. Findings [read: pp.8, 207, 222-224, 351]: - Poincare appears only on pp.222-224, for the electron's stress and its stability (sections 181-182, the Palermo 1906 paper), and in the index. The book does not credit him with the transformation, its group property or the principle of relativity. - The transformation is credited to Voigt in the footnote on p.207; the interpretation of the transformation as a statement about space and time to Einstein (sections 189-194). - Larmor is named once, in the 1909 preface, among authors whose work "is not mentioned". This is a fact about the book. The book gives no reason for it, so the priority question stays outside the physics verdicts. It is single-source evidence (the author's own text) and is stated as such. It does not contradict Lorentz's footnote that Voigt "escaped my notice all these years" (absence-of-evidence item 3).

(c) Ehrenhaft and the elementary charge (Note 16*, 1915)

Lorentz's note (PDF pp.259-260, deep read section 8): "Millikan has found values for e which can be considered as multiples of a definite elementary charge. Ehrenhaft, however, has been led to the conclusion that in some cases the charges are no multiples of the elementary one and may even be smaller than it. The question cannot be said to be wholly elucidated." References: Ehrenhaft, Wiener Sitzungsber. IIa 128 (1914) p.58; Millikan, Phys. Zeitschr. 11 (1910) p.1097 [read]. So a contested anomalous experimental result is recorded by the author as open in 1915. It is outside the seven claims, so no verdict is assigned here. It does bear on claim 3: Chapter I sections 33-35 turn e/m into a mass and a radius by assuming one common unit charge, so a different e would change them in proportion (m is proportional to e, and R, which goes as e^2/m, to e) [calc, deep reader]. The later history (Millikan-Ehrenhaft dispute, the later explanation of the sub-electron results, criticism of Millikan's data selection) is [memory, medium] and is not weighed here; it is a target for the Investigator, and nobody should read this entry as a statement of how the dispute ended.

(d) Material restored to the record

• Trouton-Rankine 1908 (no effect of motion found with a charged capacitor, bearing on whether the contraction acts on electromagnetic bodies), physicist and contrarian files: now in claim 2 above [web, as reported by those reviewers; I did not open the page].
• Glitscher 1917 (hydrogen fine structure, a later test of the mass law), mathematician, contrarian, sites.md: now in claim 3 above [web as reported].
• Wolz 1909: appears in Lorentz's own list of e/m values, see (f); Bestelmeyer's dispute is already kept.
• Columbia lectures: Chapter V ("Optical Phenomena in Moving Systems") was given on 26-27 April 1906, in a series that began 23 March 1906 [web, Columbia Spectator, sites.md]. E. B. Wilson's 1917 review of the second edition (Bull. AMS 24) is a record not yet read (landing page only, sites.md).
• Note 75* (1915): Lorentz states that relativity requires all forces, gravitation included, to propagate with the velocity of light, and concedes that forces depending only on distance do not obey the law [read: deep read pp.337-340]. A testable consequence he draws; no reviewer weighed it. I add it to claim 6's record without a separate verdict (gravitational propagation speed is outside the book's evidence).
• Section 177, a residual effect: if the sun is at rest in the ether, sunlight D-lines and a terrestrial sodium flame differ in frequency by a relative factor of order w^2/c^2, which Lorentz calls "of a purely theoretical interest" [read: deep read p.218]. The one second-order ether effect his theory leaves for celestial sources.
• Section 50 and Note on metals: Lorentz notes that his stricter electron theory makes the Drude thermal-to-electrical conductivity ratio agree worse than the cruder one, and says the earlier agreement may be "a fortuitous coincidence" [read: digest pp.75-76]. Digest-only.
• Schmelzer 2012, Arminjon and Clube 1980 stay in claim 6; the primer should add them to its further reading.

(e) Brace confirmed in the primary (QE check 6)

Brace's 7.8e-13 sensitivity and "about 1600 times greater than the smallest effect" are both in his 1904 paper [web: https://en.wikisource.org/wiki/On_Double_Refraction_in_Matter_moving_through_the_Aether, fetched as text and grepped by QE]. The earlier fetch had returned only a model summary, so this closes that gap. Brace writes "this 30 metres of water" for the light path; the 28.5 m from Wikipedia is a secondary figure. Claim 4's verdict is unchanged. QE also re-rendered p.228 (a fourth page-image check): 10^-12 is printed. The corrections to claims.md, facts.json and the deep read are still unapplied (list below).

(f) Deep reads folded into claims 3 and 7 and the 1906-1909 question

Zeeman 1914-15 (Notes 69, 69*), now read from page images pp.328-329. Lorentz's table [read: page image p.329; observed shifts in fringe spacings]:

Ratio of the 4500 and 6870 shifts, which cancels errors of flow speed and column length (Zeeman's remark): observed 1.616; 1.572 without the dispersion term; 1.608 with it [read: p.329; all three reproduce from the table, deep reader]. The number 0.826 +/- 0.007 used in the evidence table is confirmed. Caveats I keep beside it: (i) it is Lorentz's report of Zeeman (Proc. Amsterdam Acad. 17 (1914) p.445; 18 (1915) p.398), not the primary paper; (ii) Lorentz is an interested party, since the formula is his own; (iii) agreement is with the dispersion-corrected value; the plain Fresnel value is off by 0.040 at 4500 A, about 5.7 times the quoted error, and the 6440 row (one observation) is the worst fit to the corrected value (0.009) [calc, deep reader; the kind of quoted error is not stated]; (iv) the 0.826 is a fringe shift, not the drag coefficient (0.438 Fresnel, 0.451 with dispersion for water at the D line, p.328). Note 69 adds that Michelson and Morley's 1886 value was 0.434 +/- 0.02, below both 0.438 and 0.451 but within the quoted error of both, so it cannot separate them [read: p.328]; Lorentz in the main text says that taking the dispersion term into account makes the agreement with Michelson-Morley "somewhat worse; it remains however fairly satisfactory" (pp.199-200). That unfavourable detail is part of the record: the dispersion correction is supported by Zeeman (1914-15, as Lorentz reports) and not by the 1886 data.

Chapter I and the 1906-1909 change of mind (question 1 of "Absence of evidence"). New facts [read: pp.51-52, 221-222, 348]: 1. In Chapter I Lorentz reads Kaufmann's 1906 numbers as fitting Abraham's formula (69) within error, adopts "Kaufmann's conclusion, or hypothesis ... that the negative electrons have no material mass at all", and calls this "one of the most important results of modern physics". He says a material mass of about 1/100 of the electromagnetic one cannot be excluded, and drops it "with a view to simplicity". 2. In section 179 the same data are "decidedly unfavourable" to his deformable electron, though "very likely that we shall have to relinquish this idea altogether" is hedged ("it is, I think, worth while looking into it somewhat more closely"). The same 1906 data thus support "no material mass" under both models; they separate the models only through which formula fits, (69) or (313). 3. The reversal is in notes: the 1915 footnote to section 179, "This can no longer be said now", and Note 86 (Bucherer 1908, Hupka 1910, Schaefer and Neumann 1913, Guye and Lavanchy 1915; "in all probability, the only objection ... has now been removed"). Chapter I carries no 1915 note on the "wholly electromagnetic" statement, so a 1915 reader meets the 1906 position there unqualified. The deep reader found no 1915 statement that Kaufmann's measurements were wrong, as opposed to superseded. Effect on the competing explanations in absence-of-evidence item 1: nothing new decides between (a), (b) and (c). What changes is that the book itself shows Lorentz held two positions at once for years (no material mass, formula (69), in Chapter I; formula (313) in section 179), so the 1906 "decidedly unfavourable" was a statement about one formula, not about the electromagnetic nature of mass. Chapter I also lists contemporary e/m values (in units of 10^7 with the factor c sqrt(4 pi)): Simon 1.878, Kaufmann 1.823 (by Abraham's formulae), Bestelmeyer 1.72, Bucherer 1.763, Wolz 1.767 (page image; the text layer misprints Bucherer as 1.768 and p.518) [read: page image p.53]. The spread is about 9% around the adopted 1.77. It is a number a reader can use to judge the precision of the period's experiments (see "What would settle it", claim 3).

Lorentz's numbers (section 35). Hydrogen atom 1.5e-24 g; electron charge 1.5e-20 c sqrt(4 pi); m = 7e-28 g; R = 1.5e-13 cm [read: page image p.55; the text layer misprints the electrochemical equivalent as 0.0001086, the image reads 0.0001036]. The deep reader notes that these three are not mutually exact under (72): from m = 7e-28 g, R = 2e^2/(3 m c^2) is 2.1e-13 cm, not 1.5e-13 cm [calc]. I reproduced the 2.1e-13 [calc: 2 x (4.5e-10)^2 / (3 x 7e-28 x 8.99e20)]. The two agree within a factor of 1.4, which fits Lorentz's own "not far from the truth". It is an inconsistency of rounding in a background passage, not of the theory, and no verdict depends on it. Modern values (electron mass 9.11e-28 g, classical radius 2.82e-13 cm) are [memory, high].

(g) Claim 7: the parts that now rest on deep reads

• Long-wave law (148). Lorentz derives F = 16 pi alpha T / (3 lambda^4) for the ratio of emissivity to absorption from free-electron impacts in a metal (sections 60-68), with alpha = (3/2) k. It equals the large lambda T limit of Planck's formula (132), 8 pi k T / lambda^4: 16 pi (3k/2) T / 3 = 8 pi k T [calc, deep reader, reproduced]. The same result follows from equipartition of energy in an ether-filled box (sections 69-74), which Lorentz calls "a result agreeing exactly with (148)". The coefficient in (147) has one fraction not certain at the image resolution; (148) is clear. Verdict Established for the Rayleigh-Jeans long-wave limit, as before.
• Jeans's difficulty and the three exits (section 76). Lorentz sets out the ultraviolet problem (ether with unlimited degrees of freedom; "no appreciable part of the total energy shall be found" in the body) and three ways out: infinite degrees of freedom in matter (rejected, since it would require an impossible specific heat), a structured ether, or abandoning equipartition as a general law, in which case one must explain why it holds for long waves. Note 42 (silver in the dark) gives a number a reader can check: silver reflects about 90% so its absorption is 1/10; a black body at 15 C (288 K) would emit 288/1473 = 0.196, about 1/5, of one at 1200 C (1473 K) if emissivity at fixed wavelength went as T (Jeans); hence silver would emit (1/10)(1/5) = 1/50 of a white-hot body, which "ought certainly to be visible in the dark" [read: page image p.296; arithmetic reproduced, 0.0196]. He concludes the only formula that accounts for the facts is Planck's, with a different kind of link between matter and ether at short waves. The deep reader's own addition (not Lorentz's): Planck's formula at 580 nm gives a ratio of order 1e-30, so silver would emit nothing detectable [calc, deep reader, not reproduced by me]. Note 42* (1915) says equipartition "in all probability" holds for systems obeying ordinary dynamics and electromagnetism, so "a profound modification of fundamental principles" is needed: the failure is in the dynamics, not the statistics [read: p.298]. This reverses the hope in section 76 that equipartition might simply fail, and Lorentz records the reversal himself. Verdict: Historically superseded but instructive for the classical short-wave picture, as before.
• Fresnel's coefficient from the electron model (sections 156-163). Two derivations: continuous charge (equations 258-270, giving c^2/v'^2 = c^2/v^2 + 2w/v', so v' = v - w/mu^2) and molecular (corresponding states and local time, 1/v' = 1/v + w_n/c^2); both first order in w/c, both needing the elastic and resistance constants unchanged by the motion (p.197). The algebra v' + w = v + w(1 - 1/mu^2) was checked by the deep reader [calc, reproduced in outline by me]. The exact relativistic velocity-addition derivation (von Laue, 1907) reproduces this to first order [memory, high; not rechecked on the web]. Verdict Established (first order; Zeeman supports the dispersion term, see (f)).
• The parts of claim 7 still resting on digests alone are the Zeeman splitting, the Lorentz-Lorenz law, dispersion theory and Faraday rotation. The Established label for them rests on later physics [memory, high] and on the digests, not on a deep read.

(h) Claim 8: Stokes's dragged ether and Planck's condensed ether (new; no reviewer covered it)

Why it belongs: the reader of alternative science will meet the idea that the earth drags the ether, and Lorentz weighs it in the book (sections 146-149, Notes 65-68). It was digest-only; the new deep read covers it. Stated fairly, in Lorentz's words and numbers [read: pp.178-183, 325-326, page images]: - What it explains. Stokes (1845): the ether around the earth moves with the earth, with no slip at the surface. Aberration then follows at once; Lorentz says it would explain, "without any mathematical formula", everything observed "if only we could reconcile with each other its two fundamental assumptions" (p.185). - The internal difficulty. For an incompressible ether, irrotational flow plus equal normal velocities forces a slip at the sphere's surface: the relative velocity at the equator is 3/2 of the sphere's speed (Note 66; phi = -(1/2) R^3 w x / r^3; at x = 0, r = R the velocity is -(1/2)w against the sphere's w) [read: p.325; checked by differentiation by the deep reader]. For the earth's orbital speed (about 30 km/s), that is about 45 km/s of slip [calc, deep reader], not dragging at all. - Planck's repair, worked out by Lorentz (1898-99). Let the ether be a gas, compressed near the earth by gravity. Note 67: log k = mu omega / r + log k0; for X = mu omega / R = 10 the equatorial slip is 0.011 of the stream speed with a density ratio e^10 = 22,026; for X = 11, 0.0056 with e^11 = 59,874. The deep reader recomputed these from the printed formulas with SymPy (0.01138 and 0.005564) and found the potential satisfies the continuity equation. [read: p.326; calc]. The main text says e^11 gives "no more than one half percent"; that is the rounded 0.56%. - Lorentz's judgement. "this assumption of an enormously condensed ether, combined, as it must be, with the hypothesis that the velocity of light is not in the least altered by it, is not very satisfactory", while he praises Planck for it and says "we must be careful not rashly to reject a new idea"; he adds that Planck himself "is inclined to prefer the unchangeable and immovable ether of Fresnel" (pp.182-183). That is a judgement of plausibility, not a refutation. The condensation constants mu and omega are not given any physical justification in the note. - What is not in the book on these pages. The pages do not argue that the dragged ether fails against Fizeau's partial drag or against any later test; Lorentz brings Fizeau and Michelson-Morley in at sections 163-164 in support of Fresnel's coefficient. Final verdicts (provisional): - Stokes's form (incompressible, irrotational, no slip): Internally inconsistent, shown by Lorentz's calculation (Note 66), reproduced by the deep reader. - Planck-Lorentz condensed ether: Plausible, untested as a model. The mathematics is consistent (recomputed). Its two special assumptions (a 10^4-fold ether density near the earth with no change in the speed of light; the unexplained mu omega) are ad hoc, and its fit to later experiments is not weighed by any of the three reviewers. [memory, medium: later tests such as rotating-mass experiments and the Michelson-Gale experiment bear on dragged-ether ideas; I did not check them on the web in this revision, so no stronger verdict is given.] What would settle it: a review of what experiments after 1906 say about ether drag near large masses (Lodge, Michelson-Gale, Sagnac-type tests), with sources; none was done here.

Corrections to earlier documents (QE revision; for the orchestrator)

1. Still unapplied from the first pass: Brace's reach is 10^-12 (claims.md claim 4; facts.json Ch. V second part summary and key claim 5; deep read section 7 and reader summary item 3). QE re-confirmed with p.228.
2. Still unapplied: arbiter corrections 2-6 to claims.md and facts.json (see "Corrections to earlier documents" above), with correction 4 now worded "1/20 certainly, probably 1/40 (1887)".
3. Michelson-Morley 1887 bound in contrarian.md (Correction 3) and primer.md (§3.2, evidence-table row 2): replace "about 1/40 (0.02 against 0.40)" by "certainly below 1/20 (at most 0.02 of 0.40), probably below 1/40". The arbiter's own earlier wording, in this file, is corrected above.
4. Digest .08, line p.206: reads "u_x' = u_x"; the page image has u'_x = k^2 u_x (eq. 289) [read: page image p.206]. Add to the digest-error list in claims.md.
5. Digest .12, p.326: the density ratios are e^10 and e^11 (22,026 and 59,874), not "e or e1"; the sliding values are 0.011 and 0.0056 for X = 10 and 11. Digest .07, p.182: "<1 times" is e^11. Note 66: the sliding is 3/2 w [read: pages 182, 325, 326].
6. Chapter I numbers from the text layer: electrochemical equivalent of hydrogen is 0.0001036/(c sqrt(4 pi)) (not 0.0001086); Bucherer's e/m footnote is p.513, value 1.763 (not 518, 1.768); the hydrogen-atom mass is 1.5e-24 g [read: page images pp.53, 55].
7. facts.json "Notes 1-61" entry: text_available "partial" should be "yes"; add Note 16* (Ehrenhaft and Millikan), the Chapter I Kaufmann statement (pp.51-52), the e/m list, and the section 35 numbers; add section 177 and Note 75*; add the Poincare, Larmor and Voigt citation facts to the Chapter V second-part entry; fold in Notes 65-69*, 38-42*.
8. Digest-only status of the arbiter's "Source gap" paragraph at the head of this file: it now holds for Chapters I-IV except §§26-36 and 58-76, and for Chapter V §§146-160, which were deep-read in this revision.
9. primer.md (for the primer author, not changed by this file): the 1/40 wording; the evidence-table row 7 figure (confirmed, add the "with the dispersion term" caveat); one line on Note 75*; Ehrenhaft as a 1915 open question; who the book credits (Voigt, Einstein, Poincare only for the stress, Larmor unmentioned); Trouton-Rankine in §3.3 and the Columbia lecture dates; the silver-in-the-dark argument as a check-yourself item (numbers in (g)); a short section on Stokes's dragged ether and Planck's condensed ether with the 1.5 w calculation; Schmelzer and Arminjon-Clube in further reading.

Still open after this revision

• The web checks I did not run: the later experimental record on ether drag (claim 8); Trouton-Rankine and Glitscher beyond the reviewers' Wikipedia reports; the Millikan-Ehrenhaft outcome ((c)); von Laue 1907 ((g)). None changes a verdict on claims 1-7. Claim 8's second verdict is marked provisional for this reason.
• Reading the primary papers (Zeeman 1914-15, Brace 1904 in full, Zahn-Spees, Farago-Janossy, Bucherer 1908) remains the way to move the "Established" labels for the mass law and the dispersion term from Lorentz's reports to the original data.