Science Contrarian review: Poincare-Henri, "The New Mechanics"

Reviewer role: Science Contrarian (Step 2). Judges by experimental evidence, not consensus. Tags: [read] = the project document or Investigator files I read; [web] = checked on the web this run (URL given); [calc] = my own arithmetic (SymPy-free, plain Python in .venv); [memory] = recalled, with confidence.

No source gap: the single document (Halsted's English translation, The Monist 23(3), July 1913, pp. 385-395) has a full text layer [read: _text/TheNewMechanics-7c45ca.txt]. Its basis for the claims is this one essay plus the Investigator's finds.

What kind of project this is (read this first)

This is not an outsider's claim that was rejected. It is a lecture by the leading mathematician-physicist of his day, given at Goettingen on 28 April 1909 (the Wolfskehl lectures) [web: https://en.wikisource.org/wiki/The_New_Mechanics_(G%C3%B6ttingen); Lebon bibliography via Investigator google notes]. Most of its content was absorbed into standard physics. The parts that were not (ether as sole carrier of inertia, all mass electromagnetic, a Lorentz-type gravity law, radiative infall of planets) were replaced, mostly by calculation and by the later experiments. So the contrarian questions are: which parts were tested and by whom, how good were those tests at the time, and which "failures" were real.

Corrections to Step 1

1. Date and provenance (facts.json). facts.json gives "[memory] medium: about 1909-1910, printed in The Monist about 1910". The record is: lecture of 28 April 1909; French text in Sechs Vortraege (1910) pp. 49-58; Halsted's English in The Monist vol. 23 no. 3, July 1913, posthumous (Poincare died 1912 [memory, high]) [web: the en.wikisource URL above; JSTOR free-issue snippet via Investigator]. The Investigator's correction stands. Note that "Monist about 1910" was wrong by three years.
2. claims.md claim 1 and 4 attribute experiments loosely. The essay names no experimenter for the radium deflection experiments [read: p.3]; it names Kaufmann only for "constant real mass ... negligible" [read: p.8]. Poincare's own Lille lecture names Bucherer and Kaufmann [web: Investigator fr-wikisource note]. Kaufmann's own 1906 conclusion, as reported by Bucherer, was that relativity was disproved by his data [web: https://en.wikisource.org/wiki/Translation:Measurements_of_Becquerel_rays, as read by the Investigator]. So claim 4's use of "Kaufmann's experiments" is Poincare's reading, not Kaufmann's conclusion.
3. Unflagged numerical errors in the essay (Step 1 reported the numbers but did not check them). - "Mercury ... runs over about 100 kilometers per second" [read: p.3]. Mercury's mean orbital speed is 47.9 km/s [calc: 2 pi a / T with a = 5.79e10 m, T = 87.969 d]; at perihelion it is about 59 km/s [memory, high]. The essay's figure is about twice too large. It does not affect the argument (the point is that 1e-4 c is too slow for visible effects). - "some millions of milliards of centuries" [read: p.9]: 1e6 x 1e9 x 100 yr = 1e17 years [calc]. Step 1 left it unconverted. The essay gives no calculation behind it (Lille says the acceleration is "about a billion times smaller" than in a Crookes-tube anticathode [web: Investigator fr-wikisource note]). - The 1/200,000,000 deformation of the Earth [read: p.6; page image p.6]: v^2/(2c^2) with v = 29.78 km/s gives 4.93e-9 = 1/2.03e8 [calc]. The essay's figure is correct. - 38" and 32" carry no time unit in the text [read: p.10]. Step 1 reported this correctly. The unit is per century (see claim 5).
4. Step 1 says Michelson "verifies" the deformation (claim 3) without saying what that means. The Michelson-Morley null result is the observation the Lorentz-FitzGerald contraction was invented to explain; it cannot also be an independent verification of it. It shows that the combination (arm contraction, ether) gives no signal. It is not a separate test [web: https://en.wikipedia.org/wiki/Kennedy%E2%80%93Thorndike_experiment: Michelson-Morley can be explained by length contraction alone; Kennedy-Thorndike (1932) needs time dilation as well; Ives-Stilwell gives direct time dilation].
5. Mercury: the 38" is Le Verrier's 1859 figure, not the modern one. Le Verrier 1859: about 38" per century anomalous; Newcomb 1882: about 43" per century [web: search results, e.g. https://arxiv.org/pdf/1705.04397 and https://arxiv.org/pdf/1008.1811]. Poincare uses the older number. General relativity gives 42.998" per century for Mercury [calc: 6 pi G M / (c^2 a (1-e^2)) x orbits per century x 206265, with a = 5.79e10 m, e = 0.2056]. This is not a correction to Step 1 as such, but the "32" remaining" would be about 37" with Newcomb's value.
6. Investigator's arithmetic checked. Lorentz 1900: 162e-10 x 415 x 2.06e5 = 1.38" per century [calc], matching the Investigator's "about 1.4". 415 = 100 yr / 0.2408 yr (revolutions per century) and 2.06e5 = arcseconds per radian, which I confirm. This means the essay's Lorentz law (as Lorentz computed it in 1900) did not give anything like 6". The 6" in the Lille text must come from a different (Lorentz-invariant, Poincare-type) version of the law, close to de Sitter's 7.15" [web: https://en.wikisource.org/wiki/On_the_bearing_of_the_Principle_of_Relativity_on_Gravitational_Astronomy, as read by the Investigator]. The essay says only "Lorentz's law", which hides this difference.
7. Not checked by Step 1 or by the Investigator. Whether the 6" and Bucherer passages exist in the Goettingen French original (Sechs Vortraege, 1910 pp. 49-58) or were cut by Halsted. Only the Lille version is confirmed to contain them. I did not obtain Sechs Vortraege either.

Claim 1. Mass grows with velocity; light speed cannot be exceeded; radium-projectile experiments show it

a. Mathematics: the essay has no equations; the figure on p.2 (equal segments versus shrinking segments) is a qualitative picture [read: page image p.2, per deep read]. The speed limit is introduced as an assumption ("we assume it to be impossible ...") [read: p.2], not derived. Consistent as stated. The Lorentz formula m = m0 / sqrt(1 - v^2/c^2) is in the Bucherer paper, not in the essay. b. Experiments: at 100,000 km/s (beta = 0.334 [calc]) the factor 1/sqrt(1 - beta^2) = 1.061 [calc]. In 1908 Bucherer found e/m0 constant at 1.695-1.706e7 over beta = 0.32 to 0.69 under the Lorentz formula, while the Abraham formula drifted 1.676 to 1.578; later corrected to 1.730 [web: Bucherer translation, as read by the Investigator]. Modern direct tests: Bertozzi's electron kinetic energy versus speed matches relativity [web: https://en.wikipedia.org/wiki/Tests_of_relativistic_energy_and_momentum, via search]; accelerator physics depends on it daily [memory, high]. c. Tested: yes, by Kaufmann (1901-1906), Bucherer (1908), Neumann (1914), Zahn and Spees (1938 critical re-analysis), Bertozzi (1962-64) [web: https://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments]. The early record was not clean: Kaufmann's 1906 data led him to reject Lorentz-Einstein; Bestelmeyer in the printed discussion of Bucherer's 1908 talk doubted the error control (about 10% of rays off-nominal speed; the Lorentz-Abraham difference a few tenths of a millimetre) [web: Bucherer translation]. A 2023 historical study ("Hazy Spots on Photographic Plates", Hist. Stud. Nat. Sci.) examines the data quality; I saw it in the search results (Investigator and mine) but did not open it. At the time of Poincare's lecture, the radium-beta evidence was contested, and Poincare presents it without saying so. Replicated: yes, by independent methods decades later. d. If true: nothing beyond what was already adopted; it replaced the Newtonian constant-mass second law. Verdict: Established for velocity-dependent inertia and the speed limit (modern direct tests). Split: as of April 1909 the experimental case was contested and the essay's "Thus we have ascertained" overstated it; the essay's own claim that the limit follows from an assumed postulate is a postulate, not a result.

Claim 2. Relativity principle without restriction; observers see only "apparent" time

a. Internally consistent. The Paris/Berlin synchronisation argument is a correct, simple version of the Poincare 1898 clock-synchronisation idea [read: p.4-6; web: Poincare author page via Investigator]. A hidden assumption: the claim that observers cannot know whether they move is stated as an absolute, but in the 1906 Palermo memoir Poincare called it a "postulate" that "may be either confirmed or disproved later by more precise experiments" [web: https://en.wikisource.org/wiki/Translation:On_the_Dynamics_of_the_Electron_(July), as read by the Investigator]. The essay drops this caveat ("an absolute value" [read: p.4]). b. Consistent with Michelson-Morley (1887), Kennedy-Thorndike (1932), Ives-Stilwell (1938) and the many later tests [web: Wikipedia pages above]. Together these fix the Lorentz transformation. c. Tested extensively, by many groups, replicated. d. Nothing; but the essay keeps an ether as the "vehicle of the electric waves" [read: p.5]. An ether with an undetectable rest frame makes the same predictions as special relativity; the Lorentz ether theory is empirically equivalent to it [memory, high]. So the interpretive part (apparent time versus true time) has no measurable difference. Verdict: Established for the principle itself; Not testable as stated for the "apparent time, true time unknowable behind it" interpretation (Poincare retains true time; no measurement can reach it).

Claim 3. Bodies moving through the ether are deformed; Michelson verified it

a. Consistent. Length contraction factor sqrt(1 - v^2/c^2) is about 1 - v^2/2c^2, giving the 1/200,000,000 for the Earth [calc, above]. The statement that instruments shrink too, so only a comparison with the speed of light could reveal it [read: p.6], is correct reasoning and is why the effect is not directly visible. b. Michelson-Morley null result is consistent with it, as it is with the principle of relativity. On its own it does not "perfectly verify" a specific deformation; Kennedy-Thorndike was needed to exclude contraction without time dilation [web: Kennedy-Thorndike article]. c. Michelson-Morley: by Michelson and Morley 1887 and many repeats, all null. The contraction as a physical deformation of matter by motion through an ether has no separate test. d. In relativity (as Poincare's 1906 memoir already worked out: Lorentz group, invariant x^2+y^2+z^2-t^2 [web: Investigator en-wikisource note]) contraction is a kinematic effect, not a deformation by ether pressure. It is a different interpretation, not a different prediction. Note on attribution: the essay names nobody for the contraction, and Einstein, Minkowski and FitzGerald are not named anywhere in it [read: deep read section 3]. The 1906 memoir credits Lorentz and FitzGerald by name [web: Investigator]. The omission of Einstein is a fact of the record; I draw no conclusion about motive. The Lille lecture, three months later, is the same. Verdict: Established as the kinematic length contraction of relativity (indirect tests); Historically superseded but instructive for the essay's "deformation of matter through the ether" mechanism. The "Michelson verifies it" sentence is overstated for the reason in (b).

Claim 4. Constant mass vanishes; electron inertia is the ether's; Kaufmann shows real mass null

a. The essay's argument (field energy in the ether grows with speed, so the inertia of the ether grows) is qualitative. In his own 1906 memoir Poincare found that a purely electromagnetic deformable electron is not stable and needs a non-electromagnetic constant external pressure [web: Palermo memoir via Investigator]. The essay does not mention it. So the strong form (only the ether is inert; "no matter, only gaps in the ether" [read: p.8]) is in tension with Poincare's own mathematics. b. The velocity dependence is consistent with Bucherer (Lorentz formula). The composition (all mass electromagnetic) is not what those experiments measure: e/m0 constant tells you the rest mass m0, not its origin. Abraham's rigid electron, the version that gave exactly "all mass electromagnetic", fitted worse than Lorentz's in Bucherer's data [web: Bucherer translation]. In modern physics the electron's mass is not purely electromagnetic self-energy [memory, high]; the classical electron-radius picture is not the accepted account. c. Tested only indirectly. Kaufmann's own conclusion went the other way (see Correction 2). No experiment I found isolates "real mass is null". d. Would require dropping the Higgs/rest-mass picture and any non-electromagnetic mass; and accepting an inert ether. Verdict: Tested, not supported for the strong form (all mass electromagnetic, ether only inert); Established for the weak form (inertia depends on velocity and, for forces across versus along the velocity, on direction; the longitudinal and transverse masses [web: Lille text via Investigator]). The attribution to Kaufmann's experiments is Poincare's reading and conflicts with Kaufmann's own conclusion.

Claim 5. Lorentz's velocity-dependent gravity corrects Mercury's perihelion in the right direction (38", 32" left); accelerated bodies radiate and planets fall into the sun

a. The text states no formula for Lorentz's law, so its mathematics cannot be checked from the essay. The sense of the Mercury correction is right; the arithmetic 38 - 32 = 6 is made explicit only at Lille ("6"" [web: https://fr.wikisource.org/wiki/La_M%C3%A9canique_nouvelle_(Lille)]). The essay uses "acceleration" for what is a rate of perihelion advance, and omits "per century" [read: p.10]. Mixed-up sentence: "explanation of the velocity of Mercury" [read: p.10] means perihelion motion. b. Mercury: the actual anomaly is about 43" per century (Newcomb), and general relativity (1915) gives 42.998" [calc; web: Newcomb figure, Tests of General Relativity review https://arxiv.org/pdf/1705.04397]. Poincare-type laws gave about 7" per century (de Sitter 7.15"; Wacker 7.2"; Lorentz 6.69" in 1910; Lorentz's 1900 law about 1.4" [web: de Sitter 1911; calc]). So the claim "right direction" is true and the quantity is about one-sixth. The planets-fall-into-sun argument: electromagnetic radiation needs electric charge accelerating; a neutral planet has no net charge to radiate with [memory, high]. The mechanism is not supported. By contrast, gravitational radiation exists: for the Earth-Sun system it is 196 W and the infall time is 1.07e23 years [calc, circular-orbit quadrupole formula, Peters 1964 [memory, high]], and it has been seen in orbit decay of the Hulse-Taylor binary pulsar (1974) [memory, high]. Poincare's 1e17 years is not that number; his mechanism and magnitude are not supported, though the idea that accelerated bodies lose orbital energy to radiation was later vindicated in a different form. c. Tested by calculation and observation within two years: de Sitter (1911) and Wacker (c.1909) computed Poincare's law and found about 7"; the observed anomaly stayed unexplained until 1915 [web: de Sitter article; memory, high on 1915]. This was a sound, independent test; the data (planetary ephemerides) were not manipulated or omitted in any record I have seen. Whether the Goettingen original contained the 6" is unknown (Correction 7). d. If true: gravity would be an electromagnetic leftover force (Lorentz's "Franklin hypothesis" [web: Lille text]) and the equivalence of inertial and gravitational mass would need explaining. Poincare says the question whether the attraction coefficient grows with velocity "we have no means of deciding" [web: Lille]. This is an honest statement of an open question at the time. Verdict: Tested, not supported for the Lorentz/Poincare-type velocity-dependent law as an account of Mercury (explains roughly 6-7" of about 38-43" per century; also Historically superseded but instructive, replaced by general relativity). The planets-radiate-and-fall claim: Not testable as stated (1e17 years; no mechanism given); the electromagnetic-radiation mechanism for neutral planets is not supported.

Claim 6. Classical mechanics is not finally condemned; it is the mechanics of small velocities and must be learnt first

a. Consistent. At 100 km/h the correction v^2/2c^2 is 4.3e-15 [calc]; at Mercury's 47.9 km/s the Lorentz factor minus 1 is 1.3e-8 [calc]. So classical mechanics is exact to those precisions. b. Consistent with every precision test of engineering and celestial mechanics up to the Mercury anomaly. c. Tested everywhere, daily. d. Nothing. Verdict: Established (correspondence limit). The pedagogic remark is advice, not a testable claim.

Questions on how the claims were handled

• Dismissed without testing? No. Every testable claim here was calculated or measured. The Mercury claim was tested by calculation by independent astronomers within 2 years (de Sitter, Wacker) [web]. The electron-mass claim was contested in laboratory discussions in 1908 (Bucherer, Bestelmeyer, Minkowski) [web].
• Data reanalysed or omitted? The Kaufmann/Bucherer beta-ray data were reanalysed repeatedly (Bucherer 1908, Neumann 1914, Zahn-Spees 1938) [web]. The essay itself omitted, for a general audience: the unsettled state of that data (Kaufmann's own anti-Lorentz reading), the 6" figure (in the Monist text), the Poincare stress (in the 1906 memoir), and Einstein. Whether the omission of the 6" is Halsted's or the original's is unknown. I found no record of blocked funding or blocked publication.
• Interested parties. Bucherer (author of the confirming experiment) reported Kaufmann's conclusion and listed what he saw as errors in Kaufmann's work. This is a competitor's characterization beside Kaufmann's own. A modern geocentrist book cites the essay for the relativity remark; Poincare disowned that reading at Lille ("je n'ai jamais eu une telle pensee") [web: Investigator]. Truman State offprint catalogued "approximately 1902" conflicts with 1913; undecided between a cataloguer's estimate, a different Halsted translation of the same title, or a mistitle; the printed volume line of the offprint would decide [web: https://manuscripts.truman.edu/repositories/2/archival_objects/16255]. This does not bear on any verdict.

Strongest honest case for the parts that "lost"

1. The ether is not refuted by experiment, only made redundant. Lorentz's ether theory with Poincare's local time and contraction makes the same predictions as special relativity [memory, high]. Retaining it is a choice of interpretation, not a falsified claim.
2. The electromagnetic-mass idea left a durable residue: the field energy of a charge does contribute inertia, and Poincare's stress anticipates the role of stresses in energy-momentum accounting [memory, medium]. The strong form failed; the concept did not vanish.
3. Poincare's gravity (finite propagation speed, Lorentz-covariant law) was an honest attempt that got the sign of the Mercury effect right, was checked by others, and was put aside only when a better law (1915) explained the whole 43" [web, memory high on date]. Poincare himself called the result "hardly decisive".
4. His treatment of Laplace's speed-of-gravity objection, that Laplace assumed a particular aberration-like force and so "proves nothing against Lorentz's theory" [web: Lille], is correct in outline and was a real issue for any finite-speed gravity.

Against the author (same rigour)

• Overstatements: "Thus we have ascertained that the mass depends upon the velocity" (the data were disputed in 1909); "perfectly verified" for the contraction (Michelson-Morley cannot do that alone); "Kaufmann's experiments show that the real mass is negligible" (Kaufmann concluded otherwise).
• Number errors: Mercury at 100 km/s (about 48 km/s [calc]); a planet-infall time with no derivation.
• Missing unit: "38"" without "per century".
• Missing credit: no mention of Einstein or Minkowski (cannot tell why from the record).
• Unfalsifiable as stated: "no experiment can detect absolute motion" is promoted to "absolute value" [read: p.4] although he himself called it testable in 1906.

Summary of verdicts

Not done

Did not open Sechs Vortraege (1910), Revue scientifique 1909, Physikalische Zeitschrift 11 (1910), Wacker's thesis, or "Hazy Spots on Photographic Plates" (2023); the sites.md leads for these remain open. Web checks this run: three searches (Mercury 38"/43"; Kaufmann-Bucherer-Neumann and later tests; Michelson-Morley/Kennedy-Thorndike/Ives-Stilwell).