Lorentz-HA: Science Contrarian review (Step 2)

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

Tags: [read] = the document (PDF page; book page = PDF page minus 9), [web] = URL given, [memory] = recall with confidence.

Source gap: none. The OCR text is readable; Chapter V (PDF pp.196-239) and Notes 72, 75, 86 were read from page images in the deep read, and I re-read pp.221-222, 228, 239, 330 and 348 myself.

How to read this review

This book is unusual for the project: its "inventor" is a mainstream Nobel laureate whose 1904-1909 results became (with Einstein's) special relativity. The anomaly-hunting question is therefore not "is a dismissed claim vindicated?" but three sharper ones. (1) Which of Lorentz's claims were tested, by whom, and how well? (2) The claims that lost (the ether as physically privileged, the electron as a deformable shell, the contraction as a dynamical effect of forces) were not dismissed untested: what did the experiments say, and what do they still leave open? (3) How good was the 1906-1909 evidence for the claims that won? The last matters because Lorentz himself wrote in 1906 that the best electron-mass data were "decidedly unfavourable" to what is now textbook physics. The same rigour applies to Lorentz as to his critics.

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Corrections to Step 1

1. Brace's sensitivity is 10^-12, not 10^-13. claims.md claim 4 ("Brace (sensitivity 1e-13)"), facts.json (Ch. V second part, key claim 5 "sensitivity 1e-13"; summary "1e-13 vs 2e-11"), and the deep read (section 7 and reader summary 3) all give 10^-13. The page image at PDF p.228 (book p.219) reads "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, zoomed at 400 dpi]. The text layer drops the superscript, so 10^-12 is the printed value. The arithmetic confirms it: 2e-11 / 1e-12 = 20 ("the twentieth part"), whereas 2e-11 / 1e-13 would be 200. The deep read quoted the "twentieth part" sentence beside "10^-13", and the two do not agree. Brace's margin against the rigid electron is therefore a factor of 20, not 200. It is still a clear exclusion, but a smaller one than Step 1 implies. Documents to fix: claims.md claim 4; facts.json Ch. V second-part entry (summary and key claim 5); deep/ section 7 and summary item 3.
2. Claim 3 is incomplete on dates (accepting the Investigator's correction). I checked that p.348 [read] has Note 86 [1915] as quoted. The Investigator's finding that the first edition (1909) already carried the same sentence as Note 87, resting on Bucherer 1908 alone [web: https://archive.org/details/cu31924005244615, see research/2026-10-08-internet-archive.md], is plausible and fits the 1915 footnote on p.221 ("This can no longer be said now. [1915.]"). I did not re-open the 1909 scan myself. Suggested wording: Lorentz's reversal on the deformable electron dates from 1909 (Bucherer 1908); 1915 widened the list.
3. Lorentz's description of Michelson-Morley is stronger than the record. The deep read reports Lorentz: "In no case, however, the least displacement ... was observed" [read: pp.203-204]. Step 1 repeats it as a clean null. The modern account is that the 1887 run did show small readings: the observed shift was certainly below 1/20, probably below 1/40, of the expected 0.4 fringe [corrected 2026-10-08 after QE: was about one-fortieth], and Michelson's letter put the maximum near 0.02 fringe, with an average "much less than 0.01" [web: https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment]. Lorentz also cites Morley and Miller 1905: any effect "less than one hundredth part of the computed value" [read: p.204]. So "null" is a statement of an upper bound (certainly below 1/20, probably below 1/40 in 1887 [corrected 2026-10-08 after QE: was about 1/40], about 1/100 in 1905), and Miller later claimed a small positive drift (below). claims.md claim 2 should say "null within about 1/40 to 1/100 of the expected shift".
4. A framing problem in facts.json for Chapters I-IV and Notes 1-61. They rest on digests only (as claims.md admits), so nothing in this review depends on them except claim 7. I checked the digests and found no conflict. I do not endorse numerical details in them (for example e/m about 1.77e7 e.m.u., m about 7e-28 g) because I read them only in digest form.
5. Other Step 1 statements I checked and confirm [read]: "decidedly unfavourable" (p.222); the "simply postulates" passage (p.239); Note 72* "chief cause of my failure" (p.330); Note 86 as quoted (p.348); the Voigt footnote and transformation (285)-(288) (pp.206-208, from the deep read's page images); the digest corrections (297 has no 4 pi; 10^-9 n).

One derived fact worth adding to claims.md claim 4 as a check: the predicted frequency difference is (1/10) beta^2 n with beta = 1e-4, which is 1e-9 n [read: p.228]. For water the index change is 2e-11, so dn/d(ln nu) is about 0.02, which agrees with the real dispersion of water (n about 1.333 at 589 nm and about 1.337 at 486 nm: 0.004 / ln(589/486) = 0.02) [memory, medium; arithmetic mine].

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

a. Mathematics. Internally consistent for what is claimed. The free-ether equations (292), (294)-(296) keep their form [read: p.207-208]. The deep read's SymPy checks agree with the algebra for the inverse (330) and the light-signal synchronisation (Section 9-10 of the deep read). Two honest limits stand. (i) With general l, the transformed equations carry a factor (1 - w.u'_x/c^2) in div'd' and extra terms in the force (293), so Lorentz's version is not exactly form-invariant for matter. He says so in 1909 ("I have not been able to obtain ... exactly the same form") and again in Note 72 (1915) [read: pp.239, 330]. (ii) The value l = 1 is not derived from the equations. It is forced only by the mass assumptions (Sections 179 and 181 of the text; Note 75, p.337ff).

b. Experiments. Consistent with every test of the form-invariance of Maxwell's equations known to me. The transformation itself is the one tested directly in modern work: Kennedy-Thorndike (1932) and Ives-Stilwell (1938) both depend on it, and modern resonator experiments confirm the absence of an ether wind "at the 10^-17 level" (2009) [web: https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment]. Precision of the kinematics: Ives-Stilwell about 1% originally, storage-ring tests about 2e-8 (Botermann 2014) [web: https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment]; Kennedy-Thorndike-type tests to 1e-8 or better [web: https://en.wikipedia.org/wiki/Kennedy%E2%80%93Thorndike_experiment].

c. Tested? The mathematical statement needs no experiment. Its physical content (that nature obeys it) has been tested by many groups over a century and replicated. Priority note (Investigator, kept): Lorentz's own footnote concedes that Voigt (1887, "Uber das Doppler'sche Princip") used an equivalent transformation, "which to my regret has escaped my notice all these years" [read: p.207 fn.1]. Lorentz did not claim the transformation as new in this book, which is to his credit. Larmor (1900, 1904) and Poincare (1905-06) also had versions [memory, medium; the Investigator's Wikipedia notes on the priority dispute are secondary and I did not verify them].

d. If true. Nothing new beyond what is accepted. It is textbook physics. The only mainstream change Lorentz's interpretation would require is the restoration of a preferred frame, which is claim 6.

Verdict: Established (the transformation and the form-invariance of the free-ether equations). Qualifier: Lorentz's own derivation for material bodies with general l was incomplete, as he says.

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

a. Mathematics. Consistent. Check: the arm ratio L2/L1 = 1 + w^2/2c^2 (283) and the exact k = (1 - w^2/c^2)^(-1/2) agree to second order (k = 1 + w^2/2c^2 + ...). With w = 3e4 m/s (earth orbit), w^2/2c^2 = 5e-9. My check of the expected fringe shift: 2 x (22 m) x (1e-8) / (589 nm) = 0.75 for a full rotation difference, or 0.37 for one 90-degree turn, which agrees with Lorentz's 0.4 [read: p.203; the deep read made the same check]. The force relation (300) F(S) = (l^2, l^2/k, l^2/k) F(S0) is derived from electrostatics. Extending it to molecular forces is an assumption, which Lorentz flags: "we find exactly the amount of change that was postulated ... if we extend to molecular actions the result found for the electric forces" and "taking for granted that there is but one position of equilibrium" [read: pp.210-211]. These are two stated hypotheses, not derivations.

b. Experiments. Michelson-Morley (1887) bounded the effect to certainly below 1/20, probably below 1/40, of the expected shift [corrected 2026-10-08 after QE: was about 1/40]; Morley-Miller (1905) to about 1/100 [read: p.204; web as above]. Modern resonator experiments push the null far lower. Where Lorentz's proof fails: Kennedy-Thorndike (1932) used unequal arm lengths. Contraction alone cannot explain its null result: the wavelength (equivalently the clock rate) must also change by the Lorentz factor [web: https://en.wikipedia.org/wiki/Kennedy%E2%80%93Thorndike_experiment]. In 1906 this test did not exist, so Lorentz's sentence that Michelson's experiment "proves the changes of dimensions" was true only "on this assumption" (immovable ether, and nothing else compensating), as he himself qualified [read: p.205]. The claim is logically a conditional.

c. Tested? Contraction of moving bodies as a directly measured length has never been observed in the lab as such, and by the relativistic account is not a physical squeeze but a frame-dependent measurement. Its consequence (null interferometer results, to about 1e-17 in modern resonators) is tested to extraordinary precision. The original dynamical derivation ("molecular forces obey (300)") is not independently testable apart from the null results, which is a weakness I name for the inventor. Trouton-Rankine (1908) looked for an effect of motion on a charged capacitor / resistance in the rest frame and found none [web, Investigator; I did not open the primary]. This is the kind of experiment that would have separated a dynamical Lorentzian contraction from other explanations. It agreed with the transformation being exact.

d. If true. Mainstream physics already accepts the length result as kinematics. What would differ: the Lorentzian reading makes it a real dynamical effect of absolute motion through the medium. Then rods would literally shrink, and which rod is "really" shorter would have an answer. The Robertson-Mansouri-Sexl test theory (an ether frame with free contraction and dilation parameters) shows what experiments allow: all of them are met if the parameters take the Lorentz values [web via Investigator, https://en.wikipedia.org/wiki/Lorentz_ether_theory; not independently checked].

Contrarian note on the inventor. The strongest critique of Lorentz's 1895-1904 programme is that the contraction was introduced to save a null result. It is "ad hoc" in the sense of an unprovable compensation. Lorentz denied this: the 1904-1909 derivation makes the contraction follow from (300) rather than a separate postulate [read: p.211]. The honest position is that the derivation has two undemonstrated premises, and that the same results later follow from one postulate (Einstein), which is the epistemic advantage Lorentz himself concedes on p.239.

Verdict: Split. Contraction as the kinematic consequence of the Lorentz transformation: Established. Contraction as the dynamical consequence of forces obeying (300), with an absolute ether: Not testable as stated (observationally equivalent to special relativity; no measurable difference), with the 1906 claim that Michelson "proves" it: Historically superseded but instructive (it was valid only as a conditional, and Kennedy-Thorndike showed contraction alone was never enough).

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Claim 3: The electron must be a deformable (contracting) charged shell held by a non-electromagnetic Poincare stress; masses m' = k^3 m0, m'' = k m0; Kaufmann's 1906 data were "decidedly unfavourable"; later experiments confirm

This is the claim where the experimental record is most worth reading closely.

a. Mathematics. The momentum and mass calculation is consistent. G = (e^2/6 pi c^2 R) k l w; m'' = (e^2/6 pi c^2 R) k l; m' = d(klw)/dw x m0 forces dl/dw = 0 and l = 1 (313) [read: pp.220-221]. The energy problem (314)-(316) and Poincare's stress S = e^2/32 pi^2 R^4 reproduce the missing energy (e^2/24 pi R)(1 - w^2/c^2)^(1/2); SymPy in the deep read confirms [read: pp.222-223]. The inventor is honest about the weak points: stability is not shown, the sphere is unstable to shape change, and "perhaps, after all, we are wholly on the wrong track when we apply to the parts of an electron our ordinary notion of force" [read: p.224]. One more caveat I raise: the Poincare-stress model was later criticised (the "4/3 problem": the electromagnetic mass from momentum differs from that from energy by 4/3 for a non-stressed shell) [memory, medium]. Lorentz does not use that phrase, but section 180 is his version of it.

b. Experiments, and how they were handled. - Kaufmann 1901-1906. Kaufmann's 1906 data (Ann. Phys. 19, 487) fit Abraham's rigid electron and, as Lorentz writes, were "decidedly unfavourable to the idea of a contraction, such as I attempted to work out" [read: p.222]. Lorentz also wrote that "it seems very likely that we shall have to relinquish this idea altogether". He thus reported against his own theory, and did not suppress it. That is a model of conduct. Planck reanalysed nine of Kaufmann's points and found the results "not fully decisive" [web: https://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments; secondary]. Einstein's reaction, per the same page, was that the data fit Abraham's and Bucherer's theories better but their foundations seemed implausible. - Bucherer 1908 (velocity filter with perpendicular fields, radium beta source): after recalculating five runs, the Lorentz-Einstein formula gave a constant e/m, Abraham's did not [web, same page]. Wolz 1909 agreed; Bestelmeyer disputed the results [web, same page]. Hupka 1910, Schaefer-Neumann 1913, Guye-Lavanchy 1915 are listed by Lorentz as confirming [read: p.348]. - The part Step 1 does not stress. Critics later argued that these early experiments could show only a qualitative mass increase and could not decide between the competing theories: Zahn and Spees (Phys. Rev. 53, 1938) and Farago and Janossy (Nuovo Cimento, 1954/57) [web: same Wikipedia page; the page itself gives the Farago-Janossy date as 1954 in text and 1957 in references; primary papers not read]. The first experiment judged precise enough to distinguish the theories was Rogers, McReynolds and Rogers (1940), within about 1% of the Lorentz-Einstein curve [web: same page; journal reference not checked, [memory, medium]: Phys. Rev. 57, 1940]. So the weighing is: Lorentz's confidence in 1909/1915 rested on experiments the field itself later judged inconclusive; the formula was right, and the decisive precision came after Lorentz's final note. This is both a point for caution about the 1909 experimental case and a point for the formula (it survived the sharper tests). Glitscher 1917 (hydrogen fine structure) is an earlier independent confirmation [web, Investigator; secondary]. - Brace. The rigid electron predicts a double refraction of about 2e-11 in water in the earth's motion; Brace could have seen 1e-12, so he excluded it by a factor of about 20 [read: p.228, image; see Correction 1]. Lorentz hedged: "we have based our calculations on certain assumptions that could be changed for others, and Brace himself has made the calculation in a different manner" [read: p.228]. A hostile reader could say the optical argument depended on the dispersion model of Chapter IV (mass entering as m n^2). It is consistent with later results.

c. Tested? Yes, repeatedly, by several independent groups (Kaufmann, Bucherer, Hupka, Neumann, Guye-Lavanchy, Rogers, and the whole of modern accelerator physics) over 1901-1940 and since. Results: Abraham's rigid electron and Bucherer-Langevin's constant-volume electron are excluded (the latter by Brace as well, per Lorentz p.229; modern accelerators exclude both). The relativistic mass formulas are confirmed. What was not confirmed: the Lorentz-Poincare electron as a deformable shell with a non-electromagnetic stress. That model is not tested because it makes no distinct prediction (it gives the same masses as special relativity). It is also no longer needed, since in relativity the mass-energy relation is not tied to a shell model, and the electron is in practice treated as pointlike.

d. If true. For the formulas: nothing, since they are textbook. For the shell: physics would need a non-electromagnetic, unexplained binding force. Modern physics has no such model, and pointlike charge raises a self-energy problem that the shell avoided at the price of the stress.

Verdict: Split. Speed dependence of the masses, m' = k^3 m0, m'' = k m0: Established (decisive tests post-1940; the 1908-1915 tests Lorentz relied on were suggestive but later judged insufficient to decide between theories). Kaufmann's 1906 reading as an exclusion of the formula: Tested, not supported in its own right (later data and Planck's reanalysis reversed the conclusion; the original run was within 1906 error treatment, and the dispute is on record). The Lorentz-Poincare deformable shell as the physical electron: Not testable as stated (no distinct prediction; Lorentz concedes stability is not shown). Abraham's rigid sphere (the rival): Tested, not supported.

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Claim 4: Rigid spherical electrons and constant-volume electrons predict an earth-motion double refraction of about 2e-11 in water, which Brace (sensitivity 10^-12) did not see

a. Mathematics. Consistent, with one caution. h' = 1 + (6/5) beta^2, h'' = 1 + (2/5) beta^2, effective frequencies (1 - 3 beta^2/20) n and (1 - beta^2/20) n, difference beta^2 n/10 = 1e-9 n at beta = 1e-4 [read: p.227-228; the deep read's SymPy confirmed]. The step to 2e-11 in the index of water uses dn/d(ln nu) of about 0.02, and my check from the dispersion of water gives the same order (above). The assumption inside is Lorentz's: the electron mass enters the optics only via m n^2 [read: p.226]. If another assumption were made, "Brace himself has made the calculation in a different manner" [read: p.228]. A quantitative factor-of-20 margin is not large enough to be insensitive to such differences; I would say the exclusion is firm for the orders of magnitude but not exact.

b. Experiments. Rayleigh (1902, 76 cm tube) and Brace (1904, 4.13 m water column) both negative [web: https://en.wikipedia.org/wiki/Experiments_of_Rayleigh_and_Brace, via Investigator; I did not re-open it; the first claim also matches p.205 and p.228 [read]]. The Investigator adds (secondary) that Brace first read the null result as refuting contraction, and that Lorentz (1904) and Larmor (1904) showed it follows when the full transformation, time included, is used. The same point is made in section 177 of the book: "our theorem explains why Rayleigh and Brace have failed to detect a double refraction" [read: p.218-219].

c. Tested? Yes: Rayleigh, Brace. No replication found in the review files. [web] sources describe a later experiment series but I did not verify any, so I state none. Brace's method is explained in the text only in summary.

d. If true. If double refraction had been seen, the full-contraction picture (and relativity) would have needed another term, and the rigid electron would have survived. Nothing in mainstream physics changes by Lorentz's reading of the null.

Verdict: Tested, not supported (for the rigid and constant-volume electron models; the margin is a factor of about 20 for the rigid sphere, from Lorentz's own calculation, with the stated model assumptions).

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Claim 5: A moving observer, using rods and clocks shaped by the same forces, finds clocks slow by k, light speed c, light-signal-synchronised clocks reading local time; descriptions are reciprocal, so no experiment shows who moves

a. Mathematics. Consistent and checked. Round trip time 2cL/(k(c^2 - w^2)) = 2kL/c; transverse leg gives the same; with clocks slow by k the observer measures 2L/c, so c [read: pp.233-234]. Light-signal synchronisation gives t' = t/k - (w/c^2) x', identical to (288) [read: pp.234-235; deep read SymPy]. Reciprocity: the inverse of (328) is (330), so the moving observer's description of S0 is exact [read: pp.236-238]. Inventor-side caveat: the whole argument assumes the clock mechanism and the rods obey (300) and (305); Lorentz says "if we suppose the forces in the clock-work to be liable to the changes determined by (300)" [read: p.233]. This premise is an extra hypothesis, and in the Lorentzian reading it is physical.

b. Experiments. Time dilation: Ives-Stilwell 1938 first direct quantitative test, about 1%, modern storage rings to about 2e-8; notably, Ives himself preferred a Lorentz-Larmor ether interpretation over Einstein's framework [web: https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment]. Kennedy-Thorndike (1932) needs time dilation alongside contraction [web, above]. Light speed c isotropy: resonator experiments. Reciprocity (a moving frame sees the rest frame's clocks slow, not fast) is a symmetric-description claim that is tested indirectly, e.g. by the consistency of all of the above and the lack of any preferred-frame signal.

c. Tested? Yes, by many groups, replicated. The Investigator's related work, Bischoff van Heemskerck (F1000Research 12:407, 2023), argues for contraction and dilation as "purely local consequences of the relative velocity between a system and its medium", dropping reciprocity, matching the standard tests and proposing a modified Ives-Stilwell test [web via Investigator, not independently read]. I record it as a published proposal of a falsifiable alternative, not as a result. No replication or test of that proposal is on record in the review files.

d. If true. No change. Strictly, the claim as Lorentz states it (no experiment shows who moves) is the claim of the neo-Lorentzian view as well; neo-Lorentzian and special-relativistic accounts make identical predictions [web via Investigator: LET page]. Anything that broke reciprocity would require changing special relativity.

Verdict: Established (clock slowing, c isotropy, synchronisation and reciprocity as predictions, confirmed experimentally; Ives-Stilwell to about 2e-8, Kennedy-Thorndike to 1e-8 or better). The interpretive layer (that the ether-frame description is the "true" one even though undetectable) belongs under claim 6.

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Claim 6: Lorentz's comparison with Einstein: Einstein "simply postulates what we have deduced, with some difficulty and not altogether satisfactorily"; Lorentz keeps an ether of "a certain degree of substantiality"; in 1915 he says his failure came from treating t' as auxiliary

a. Mathematics. This is an interpretive claim, but the mathematical point inside it is checkable: Lorentz's equations for moving axes are not exactly form-invariant, whereas Einstein's are with l = 1 and relativistic velocity and density [read: p.239; Note 72, pp.330-334]. Note 72 confirms Lorentz took this to be the real difference.

b. Experiments. None distinguishes the two interpretations. Lorentz says so: "It would be impossible to decide which of them moves or stands still with respect to the ether, and there would be no reason for preferring the times and lengths measured by the one to those determined by the other" [read: p.238]. The physical content of the ether claim is whatever is added to the transformations, and so far nothing has been found. Einstein (Leiden, 1920) said the Lorentzian ether retained only immobility, and that SR removed that as well while allowing an ether "in a non-mechanical sense" [web: https://en.wikisource.org/wiki/Ether_and_the_Theory_of_Relativity]. That is Einstein's characterization, and he is an interested party in the dispute. Lorentz's own later statements (Investigator): in 1913 the abolition of the ether is "to a certain degree a dispute about words" and "it will depend ... on the way of thinking one is used to" [web: archive.org bub_gb_89PPAAAAMAAJ; Investigator's cleaned translation of noisy OCR, not re-read by me]; and at the 1927 Mount Wilson conference "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 to be checked].

c. Tested? Not testable: this is a difference of interpretation with no measurable consequence, unless a preferred-frame effect appears. Preferred-frame tests (Robertson-Mansouri-Sexl framework; modern resonators) are the experiments that bear on it, and they find nothing, with bounds of 1e-8 to 1e-17 depending on the observable [web: pages above]. Dayton Miller (Investigator): Lorentz corresponded with Miller in 1906, 1921 and 1926 and lectured on Miller's repetitions in 1925-26; Miller reported a small positive drift of roughly 10 km/s in the 1920s, versus about 30 km/s if the earth's orbital motion were fully seen. Nobody has replicated it, modern experiments rule it out, and a reanalysis (Roberts 2006) found his signals statistically insignificant [web: https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment; I did not open Roberts or Shankland 1955]. I record it because it is the one anomalous-result line connected to this book's central experiment and Lorentz took it seriously enough to discuss it. It is evidence that was weighed and not found to hold up.

d. If true. Lorentz's preference (ether-fixed rods and clocks as the "natural" standard) would, if physically meaningful, require a privileged frame that nature hides perfectly. Mainstream physics would need to accept a conspiracy of compensations, which is the objection raised since 1895. Lorentz's own answer is that the compensations follow from the common electromagnetic character of the forces [read: pp.210-211; Note 75, pp.337-340], which Note 75 extends to a requirement that gravitation propagate at c (a strong hypothesis in 1915, later borne out only in the sense of general relativity and the 2017 binary-neutron-star limit, which I mention from [memory, high] and have not sourced further).

Weighing for the reader. The neo-Lorentzian literature the Investigator found (Janossy 1971, Prokhovnik 1967, Ives, J. S. Bell's teaching approach, Schmelzer 2012, Arminjon, Clube 1980) keeps a preferred frame with complete Lorentz transformations and is empirically equivalent to SR [web via Investigator; Wikipedia's label "unfounded within the mainstream" is that page's characterization, which I report as such]. Nothing found in the review files tests it apart from SR. It is fair to say that the debate rests on parsimony and on research programmes, not on data.

Verdict: Not testable as stated (the ether-substantiality reading; no measurable difference from SR). Lorentz's historical self-assessment (Einstein's presentation is simpler; his own failure was the status of t'): Historically superseded but instructive.

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

a. Mathematics. Not re-derived by me; these chapters rest on digests (see Source gap). The structure described (damped oscillator, E + (4 pi/3) P local field, (mu^2 - 1)/(mu^2 + 2) proportional to density, Zeeman triplet) is the standard classical derivation and I have no reason to doubt the digest [read: digests pp.107-176, 77-106].

b. Experiments. Zeeman (1896) normal triplet and e/m of the same order as cathode rays; Lorentz-Lorenz law; dispersion. Real limits stated by Lorentz and the digests: complex (anomalous) Zeeman patterns are not explained by the simple models (Lorentz calls them illustrations); the equipartition result runs into Jeans's difficulty (ultraviolet catastrophe). Quantum theory, not classical electrons, now accounts for those [memory, high].

c. Tested? Yes, extensively, by Zeeman and many others, replicated. Zeeman's own 1914-15 repetition of the Fizeau experiment agreed with the dispersion-corrected calculation (0.826 +/- 0.007 observed at 4500 A, as digested; the table is partly garbled [read: digest, Note 69*]).

d. If true. Already accepted as classical electron theory; replaced at the atomic level by quantum mechanics.

Verdict: Established for the normal Zeeman effect, Lorentz-Lorenz law, classical dispersion and the Rayleigh-Jeans long-wave limit. Historically superseded but instructive for the classical oscillator as an atomic model and the complex Zeeman patterns.

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How the claims were rejected: the record of dissent

• Not dismissed without testing. Every Lorentz claim that lost did so in the laboratory or by a better theory. Kaufmann's data first went against Lorentz in 1906, and Lorentz said so himself. Brace excluded the rigid-sphere rival. Bucherer (1908) and later work reversed Kaufmann's verdict. This is not a case of suppression.
• Data handling worth knowing. Planck found Kaufmann's data "not fully decisive" on re-analysis, and Bucherer's 1908 result came from recalculating five runs [web, secondary]. Bestelmeyer disputed Bucherer's results [web, secondary]. Later authors (Zahn-Spees, Farago-Janossy) argued the 1908-1914 experiments could only show a qualitative increase. I did not read the primary papers; I flag them as the records that would settle how good the 1908-1915 case was. Rogers et al. (1940) is the first precise test.
• The interpretive loser (the ether as physically privileged) was not refuted but made unnecessary. Lorentz himself calls the choice partly "a dispute about words" (1913) [web, Investigator]. No funding or publication blockage is documented in the review files; the Investigator found none. Lorentz held a Nobel Prize (1902) and a leading position throughout, so it is not a suppression story [memory, high; not needed for any verdict].

Strongest honest case for the claims, including inconvenient points

1. Lorentz derived, in 1904-1909 from field equations plus stated hypotheses, the contraction, time dilation, local time as synchronised time, relativistic masses, the light speed c measured by a moving observer, and reciprocity, all in this book [read: pp.206-238]. Priority questions aside, the physics of the transformation is correct.
2. He reported evidence against his own model (Kaufmann) and conceded the model's weak points (instability, "wrong track") [read: pp.222-224].
3. Special relativity's kinematics and Lorentz's ether theory are empirically equivalent, so the Lorentzian reading has not been refuted by data; it has been displaced by economy of postulates and by general relativity [web: https://en.wikipedia.org/wiki/Lorentz_ether_theory via Investigator].
4. Ives, an experimentalist who confirmed time dilation, never gave up a Lorentz-Larmor interpretation [web: https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment].

Where the inventor is weak

1. The contraction rests on two stated hypotheses (molecular forces obey (300); equilibrium is unique), and the "proof" from Michelson-Morley was conditional [read: pp.205, 211].
2. The deformable electron needs an unexplained Poincare stress and is unstable; Lorentz concedes it [read: pp.223-224].
3. The 1909 experimental confidence (Note 87, Bucherer 1908) rested on a measurement later judged inconclusive.
4. The brace margin is about 20, not 200, and depends on the m n^2 dispersion assumption.
5. His equations for matter with general l were not exactly invariant, a point he admitted.

Investigator findings kept in the record (whatever the verdict)

• First edition (1909) Note 87 already confirms (313) on Bucherer 1908 alone: claim 3.
• Das Relativitatsprinzip (1913/14): ether as "a dispute about words"; reservation about the light-speed limit: claims 5-6.
• 1927 Mount Wilson statement ("heuristic working hypothesis"): claim 6.
• NHA archive 364 items (ether treatise, Bucherer note 1908-09, Kaufmann 1904, Morley 1904, Miller 1906, Voigt 1888 letters, Einstein letters 1909-1927): records not yet read.
• Zahn-Spees 1938, Farago-Janossy 1954/57, Rogers 1940, Glitscher 1917, Potters (HSNS 2023) on the early electron-mass experiments: claim 3.
• Kennedy-Thorndike 1932, Trouton-Rankine 1908, Ives-Stilwell 1938: claims 2 and 5.
• Neo-Lorentzian literature (Janossy, Prokhovnik, Ives, Bell, Schmelzer, Arminjon, Clube; Bischoff van Heemskerck 2023): claims 2, 5, 6.
• Dayton Miller's drift and Lorentz's correspondence with him: claim 2 and 6.
• Columbia 1906 lectures (Chapter V given 26-27 April 1906), Kox's correspondence volumes, Wilson's 1917 AMS review: historical record.

What would settle the open points

• Read Zahn-Spees (1938) and Farago-Janossy (1957) to quantify how far Bucherer 1908 and Neumann 1914 actually constrained Abraham versus Lorentz.
• Read NHA archive 364 (Bucherer 1908-09, Miller 1906/1921/1926, Voigt 1888) for what Lorentz knew and when.
• Check the Mount Wilson 1927 wording against the ApJ scan.
• Obtain Brace's 1904 paper to confirm his sensitivity (10^-12 per Lorentz) and his own calculation.

Verdict summary