Lorentz-HA: central claims
Project: H. A. Lorentz, The Theory of Electrons and its Applications to the Phenomena of Light and Radiant Heat (2nd ed., Teubner 1916; lectures at Columbia University, 1906; text of 1909 with [1915] notes). One document, 361 PDF pages, OCR text [read]. Printed page = PDF page minus 9.
No source gap: the text layer is readable. Formulas are often garbled in the OCR; the central Chapter V (PDF pp.196-239) and Notes 72, 75, 86 were read from page images in the deep read, so the claims below rest on [read] text, not [memory]. Chapter I sections 26-36, section 179 and Notes 13-17, Chapter II sections 57-76 with Notes 38-42, Chapter V sections 146-163 with Notes 65-72, and Note 69 were deep-read after QE (2026-10-08). Chapters III-IV and the rest of the Notes rest on digests only (peripheral to the claims).
- A body moving through an immovable ether is described by the exact transformation x' = kl(x - wt), t' = kl(t - wx/c^2) (k = 1/sqrt(1 - w^2/c^2)); with l = 1 this is the modern Lorentz transformation, and it leaves the free-ether Maxwell equations in the same form. Caveat: 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*), and reciprocity needs l = 1. [read: PDF pp.206-208, 236, 239, 330]
- If molecular and elastic forces transform like electrostatic forces, matter moving through the ether contracts by k along its motion, so the Michelson-Morley experiment is expected to give a null result: observed shifts were certainly below 1/20 of the expected 0.4 fringe in 1887 (at most 0.02), probably below 1/40, and below 1/100 in the Morley-Miller experiments. Lorentz's wording is conditional: with an immovable ether, Michelson's experiment "proves" the contraction. [read: pp.204-205, 210-214; web: https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment]
- The deformable (contracting) electron, held together by a non-electromagnetic Poincare stress, gives speed-dependent masses m' = (1 - beta^2)^(-3/2) m0 and m'' = (1 - beta^2)^(-1/2) m0; Lorentz presents this as the model that fits the relativity principle, not as proved: stability is not shown. "Wholly electromagnetic" mass holds for the momentum only; with the stress, a quarter of the rest energy is stress energy. In Chapter I he adopts "Kaufmann's conclusion, or hypothesis" that the negative electron has no material mass (about 1 percent not excluded) for simplicity. In 1906 Kaufmann's data were "decidedly unfavourable" to the deformable electron (they agree with Abraham's rigid sphere); his reversal dates from the 1909 edition (Note 87, Bucherer 1908), and in 1915 (Note 86) he cites Bucherer, Hupka, Schaefer and Neumann, and Guye and Lavanchy as confirming these masses. [read: pp.51-52, 219-225, 348]
- Rigid spherical electrons (Abraham) predict an earth-motion double refraction of about 2e-11 in water; constant-volume (Bucherer-Langevin) electrons an effect "even a little stronger". Brace's experiment, whose reach Lorentz puts at 10^-12 (about one twentieth of the prediction), did not see it. [read: page image pp.228-229; Brace's own paper: 7.8e-13 and "about 1600 times greater than the smallest effect", web: https://en.wikisource.org/wiki/On_Double_Refraction_in_Matter_moving_through_the_Aether]
- A moving observer, using rods and clocks shaped by the same forces, finds clocks slow by k, light speed c, and clocks synchronised by light signals reading local time; the descriptions of an ether-rest observer and a moving observer are reciprocal, so no experiment shows who moves. [read: pp.232-238]
- Lorentz's own comparison with Einstein: Einstein "simply postulates what we have deduced, with some difficulty and not altogether satisfactorily"; Lorentz still regards the ether as having "a certain degree of substantiality" and prefers ether-fixed rods and clocks, while in 1915 (Note 72*) he says he failed through treating t' as only an auxiliary "local time". The book credits Voigt for the transformation (p.207 footnote), Einstein for the interpretation, Poincare only for the electron stress (pp.222-224), and names Larmor only in the preface (p.8); it gives no reasons. [read: pp.8, 207, 222-224, 238-239, 330, 351]
- (Background) The electron theory reproduces the Zeeman effect, the Lorentz-Lorenz refractivity law, dispersion, Faraday rotation and the long-wave black-body law. Deep-read specifics: Jeans's equipartition law would make silver glow visibly in the dark (Note 42), so Lorentz concludes only Planck's formula fits and, by 1915 (Note 42), that radiation theory needs a profound modification of fundamental principles; Zeeman's 1914-15 Fizeau repetition (Note 69) matches the dispersion-corrected drag (0.826 +/- 0.007 observed against 0.825 calculated at 4500 A; Fresnel-only 0.786); Stokes's dragged ether is internally inconsistent and Planck's condensed ether (sliding 0.011 w0 to 0.0056 w0, density ratio 2e4 to 6e4) is "not very satisfactory". As an open item Lorentz leaves in 1915, Millikan's charges are multiples of one elementary charge while Ehrenhaft finds some that are not and may be smaller (Note 16*): "The question cannot be said to be wholly elucidated." [read: pp.87-106, 182-183, 259-260, 296-299, 325-329]
Corrections to earlier documents: the deep reads list these digest errors; facts.json uses the corrected values. (1) Digest .09: m', m'' at p.221 (m' = k^3 m0, m'' = k m0, "iota" is the letter l); "10^-8 n" at p.228 should be (1/10) beta^2 n = 1e-9 n. (2) Digest .08: p.208 eq. 297 has no 4 pi; p.206 gives "u_x' = u_x" but the page image has u'_x = k^2 u_x (eq. 289). (3) Digest .07 p.182 and .12 p.326: the density-ratio exponents were dropped by OCR; they are epsilon^10 (about 22,026) and epsilon^11 (about 59,874), sliding 0.011 w0 and 0.0056 w0. (4) Text layer: electrochemical equivalent of hydrogen 0,0001036 (not 0,0001086), Bucherer e/m footnote p.513 value 1,763 (not 518/1,768). (5) Earlier claims.md and facts.json carried Brace's reach as 1e-13; Lorentz's printed figure is 10^-12 (p.228 image); Brace's own 7.8e-13 is a different statement. (6) The earlier "about 1/40 (0.02 fringe against 0.40 expected)" for Michelson-Morley 1887 was internally inconsistent (0.02/0.40 = 1/20); see claim 2. (7) The text layer prints section number 176 twice; the first (p.214) is section 175.