Physicist review (Step 2): Poincare-Henri, "The New Mechanics"

Reviewer role: PhD physicist. Tags: [read] from the project document or project files; [web] with URL; [memory] with confidence. Source basis: one document, Halsted's 1913 Monist translation of Poincare's Gottingen lecture [read: p.1-11]. No source gap (text layer complete, no equations in the essay). All quotations from the essay are from deep/TheNewMechanics-7c45ca.md and _text/TheNewMechanics-7c45ca.txt.

Terms for the reader. c = speed of light, about 300,000 km/s. "Ether" = the hypothetical medium that carried light waves. beta rays = fast electrons from radioactive decay (the essay's "radium projectiles"). "Perihelion" = the point of closest approach to the Sun; its slow rotation round the Sun is "perihelion motion" or "precession". 1 arcsecond (") = 1/3600 degree.

Corrections to Step 1

1. Date and identity (facts.json says "about 1910", [memory] medium). Corrected by the Investigator and checked by me. The document is the Gottingen Wolfskehl lecture of 28 April 1909, French text printed in Sechs Vortrage (1910) pp. 49-58, English by Halsted in The Monist vol. 23 no. 3, July 1913, pp. 385-395, a year after Poincare's death in 1912 [web: https://en.wikisource.org/wiki/The_New_Mechanics_(G%C3%B6ttingen); Lebon bibliography and JSTOR snippet via research/2026-10-06-google.md]. I did not re-open these pages; I rely on the Investigator's notes, which agree across three sources. The Truman State offprint catalogued "approximately 1902" [web: https://manuscripts.truman.edu/repositories/2/archival_objects/16255] conflicts and stays unresolved (a different Halsted translation, a cataloguer's estimate, or an error). It does not affect any physics claim.
2. Claim 5's time unit. claims.md, correctly, notes that the essay states no period for 38" and 32". The essay is silent, so "per century" is an inference. It is a well-supported one: Le Verrier's 1859 figure was 38" and Newcomb's 1882 revision 43", both per century [web: https://en.wikipedia.org/wiki/Tests_of_general_relativity]. Poincare's Lille text states the 6" and 32" outright (below). I treat "per century" as established by outside sources, not by the document.
3. claims.md claim 5 says 32" is "still unexplained" and leaves the 6" implicit. The Lille lecture [web: https://fr.wikisource.org/wiki/La_M%C3%A9canique_nouvelle_(Lille)] states "un mouvement de 6''" and "une marge de 32''". The inference 38 - 32 = 6 is confirmed by Poincare himself, but only in the Lille text, not in the project document.
4. Claim 3 wording. claims.md says Michelson's experiments are "said to verify" the deformation. The essay says the third hypothesis is "perfectly verified" [read: p.7]. Physically the Michelson-Morley experiment does not verify contraction. It gives a null result that contraction (or relativity) would explain. See claim 3.
5. Claim 1 wording. The deep read notes the radium passage names no experimenter [read: p.3]. Step 1 is correct; the Lille text names Bucherer and Kaufmann.
6. Mercury speed. The essay says "about 100 kilometers per second" [read: p.3]. Mercury's mean orbital speed is about 47.9 km/s (my calculation from a = 5.791e10 m, period 87.969 d) [memory, high]. The essay is off by about a factor of 2. Harmless to the argument, since the point is only that it is far below c.
7. Step 1 is otherwise accurate. I checked the 1/200,000,000 figure (below) and the 38"/32" passages against the text.

Mainstream view, stated fairly

The essay is not a fringe claim. It is a leading mathematician-physicist's popular account, in 1909, of the Lorentz-Poincare theory that sat beside Einstein's 1905 special relativity. Mainstream physics today takes special relativity (SR) as established: the speed of light c is the same in all inertial frames, time and length depend on the observer's motion through the Lorentz transformation, and the ether plays no role. Poincare's essay gets most of the kinematics right, and it also contains statements that are wrong or outdated by today's standards (electromagnetic mass only, planets radiating into the Sun, the ether as the seat of inertia). I judge each against the experiments and calculations below.

Claim 1: Mass increases with velocity; c cannot be exceeded

a. Mathematics. The essay has no equations. The figure (p.2) shows equal velocity steps shrinking toward a limit. This is qualitatively the relativistic relation: with the Lorentz factor gamma = 1/sqrt(1 - v^2/c^2), momentum p = gamma m v, so equal impulses (equal increments of p) give smaller and smaller increments of v. The essay presents the limit as an assumption ("we assume it to be impossible...") [read: p.2]. That is consistent, not circular. Worked number: at v = 0.3178 c, gamma = 1.055; at v = 0.6879 c, gamma = 1.378 (my arithmetic). These are the first and last speeds in Bucherer's 1908 run [web: https://en.wikisource.org/wiki/Translation:Measurements_of_Becquerel_rays, via research/2026-10-06-en-wikisource.md section 6]. The essay's speed range (about one third of c, [read: p.3]) matches the low end.

b. Experiments. Consistent with the beta-ray deflection experiments (Kaufmann 1901-1906; Bucherer 1908) and, much more strongly, with a century of accelerator physics: electrons and protons never exceed c, and their momentum follows gamma m v [memory, high]. Bucherer's table (per the Investigator): Lorentz formula e/m0 constant at 1.695-1.706 x 10^7 over beta 0.32-0.69; the Abraham rigid-electron formula drifted from 1.676 to 1.578 [web: Wikisource Bucherer translation].

c. Tested. Yes. Kaufmann (1901-1906), Bucherer (1908), and later many others. Important caveat from the Investigator's finding, which I keep: Kaufmann himself concluded in 1906 that his data disproved relativity (as reported by Bucherer), and Bestelmeyer in the printed discussion doubted the sources of error (about +/-10% of rays at off-nominal speed; the Lorentz/Abraham difference "only a few tenths of a millimeter") [web: same]. So the 1908 data were contested at the time and are not a clean replication of 1909 knowledge. A 2023 study of the data quality exists ("Hazy Spots on Photographic Plates", UC Press HSNS) but the Investigator did not open it, and neither did I. The modern confirmation is independent of the 1900s plates.

d. If true: nothing; this is mainstream. It is what replaced Newton's p = m v.

Verdict: Established. Split: the essay's phrasing "mass increases with velocity" is an older convention (relativistic mass); modern usage keeps invariant mass and a changing momentum. That is a convention change, not a physics change. In 1909 the experimental evidence was real but contested (Kaufmann's own reading, Bestelmeyer).

Claim 2: Principle of relativity has absolute value; observers know only "apparent" time

a. Mathematics. The essay has none. The behind-the-scenes mathematics is Poincare's 1905/06 memoir (Lorentz transformation x' = kl(x + et), t' = kl(t + ex), invariant x^2 + y^2 + z^2 - t^2, Lorentz group) [web: https://en.wikisource.org/wiki/Translation:On_the_Dynamics_of_the_Electron_(July), via research notes]. The memoir is internally consistent as far as I can see from the Investigator's quotations; I did not recheck its equations (the mathematician's job). The Paris/Berlin clock example [read: p.4-6] is the standard synchronisation-by-light argument: if both observers move with the Earth and assume light travels equally fast both ways, their clocks are synchronised in their frame but would disagree with a frame at rest in the ether. Poincare treats this as "local time", an artefact of not knowing the ether-frame time. Einstein removed the distinction by dropping the ether-frame time altogether. Mathematically the two readings give identical predictions for any measurement of this kind. The difference is philosophical. The essay says "absolute value" [read: p.4]. The 1906 memoir calls it a postulate that "may be either confirmed or disproved later by more precise experiments" [web]. So the essay and the memoir state the status differently. I note it and do not call it a contradiction (a lecture versus a technical paper).

b. Experiments. Consistent with Michelson-Morley (1887) and its successors, Kennedy-Thorndike (varying arm lengths), Ives-Stilwell (time dilation) and Trouton-Noble. Modern optical-resonator versions limit speed-of-light anisotropy to about 10^-17; Ives-Stilwell-type ion storage ring tests limit deviations from relativistic time dilation to about 10^-8 [web: https://en.wikipedia.org/wiki/Tests_of_special_relativity, secondary summary]. Nothing detects absolute motion.

c. Tested. Yes, repeatedly, with no violation. The Lorentz-ether reading (a hidden preferred frame that nature conspires to hide) makes the same predictions as SR; no experiment distinguishes them [memory, high]. So the ether-based reading is not refuted, but it has lost on parsimony and was dropped.

d. If true: nothing; mainstream. What would change if the ether-frame reading were right: only the interpretation, since no measurable difference.

Verdict: Established for the principle of relativity (no experiment detects absolute motion). Split: the essay's ether-based interpretation of "apparent time" is Not testable as stated (no measurable difference from SR) and Historically superseded but instructive.

Claim 3: A moving body contracts by 1/200,000,000 for the Earth; Michelson's experiments verify it

a. Mathematics. Length contraction along the motion is L = L0 sqrt(1 - v^2/c^2), approximately L0 (1 - v^2/2c^2). For the Earth's orbital speed v = 29.78 km/s: v^2/(2c^2) = 4.93e-9 = 1/(2.03e8). So the essay's 1/200,000,000 is correct to its precision (my calculation) [read: page image p.6, confirmed by the deep reader]. Internally consistent.

b. Experiments. The Michelson-Morley experiment compares light travel times along two perpendicular arms. A 1/200,000,000 contraction along the motion is exactly what is needed to cancel the expected fringe shift to first order in v^2/c^2 [memory, high]. The essay says the experiments "perfectly verify" the hypothesis [read: p.7]. That is an overstatement. A null result is what contraction predicts, but it is also what SR predicts without any ether, and what an ether dragged along with the Earth would give. A single Michelson-Morley experiment cannot separate contraction from other explanations. Kennedy-Thorndike (1932) was designed to test the remaining combination and also came out null, which is consistent with contraction plus time dilation [memory, high]. In Poincare's own 1906 memoir the contraction is credited to Lorentz and FitzGerald [web, research notes]; the essay names nobody [read: p.6-7].

c. Tested. The null results of Michelson-Morley (1887), Michelson-Morley repeats by Morley and Miller, and Kennedy-Thorndike are real, replicated, and modern resonator versions are about 10^-17 [web: Wikipedia Tests of special relativity]. Contraction itself has not been measured as a standalone length change of a rigid body (it is not directly visible; rotated objects look rotated, not squashed) [memory, medium, not web-checked]. I did not use that point in the verdict.

d. If true: nothing; mainstream. The reading as a real deformation of matter in an ether is superseded: today it is a statement about how coordinates relate between observers.

Verdict: Established for the size and null-consistency (the number is right, and the experiments are consistent with it). Split: the claim that Michelson "verifies" a deformation of matter through the ether is Historically superseded but instructive (a hypothesis introduced ad hoc to save the ether; SR derives it).

Claim 4: Constant mass vanishes; the electron's inertia is the ether's; Kaufmann shows this

a. Mathematics. No equations in the essay. In the 1906 memoir Poincare found that a purely electromagnetic deformable electron is unstable and needs a non-electromagnetic "constant external pressure" (the later "Poincare stress") [web, research notes]. The essay says only the ether is inert and that "matter's constant mass has disappeared" [read: p.8]. Those two statements are not consistent unless an extra, non-electromagnetic force exists, which his own memoir says it does. The 4/3 problem is also known: the electromagnetic energy and electromagnetic momentum of the electron field give inconsistent masses [memory, high]. So the all-electromagnetic mass programme has an internal difficulty that the lecture does not mention. The direction-dependent mass (longitudinal and transverse) is correct in kind: for Lorentz's electron the longitudinal mass is gamma^3 m and the transverse is gamma m [memory, high].

b. Experiments. Kaufmann's data are used here for "constant real mass is negligible" [read: p.8]. Kaufmann's own conclusion, as reported by Bucherer, was that relativity was "disproved" [web, research notes]. So the essay uses Kaufmann's data for a conclusion that Kaufmann himself did not draw. Bucherer's 1908 data favour the Lorentz formula over Abraham's rigid electron [web]. Today: the electron is a point-like particle with measured mass 9.109e-31 kg; there is no evidence its mass is of electromagnetic origin, and the classical electron radius calculation of electromagnetic mass fails (the self-energy diverges and is renormalised in quantum electrodynamics) [memory, high]. Mass comes mostly from other mechanisms (e.g. nucleon mass from the strong interaction, electron mass from the Higgs coupling) [memory, high].

c. Tested. The velocity dependence of electron mass was tested (claim 1). The stronger claim, that all mass is electromagnetic and the ether alone is inert, was not tested as stated; it was dropped when the ether was dropped and when other mass sources were found. I have no source for a specific test of "purely electromagnetic mass" and do not assert one.

d. If true: the Standard Model's mass sector would need replacing, and the idea of a medium (the ether) as the carrier of inertia would return, contradicting the Lorentz invariance experiments of claim 2.

Verdict: Split. Velocity-dependent mass: Established (see claim 1). "All mass is electromagnetic, the ether alone is inert": Historically superseded but instructive; it conflicts with its own author's 1906 requirement of a non-electromagnetic stress. Kaufmann's data as support: contested (his own reading differed); I keep that in the record.

Claim 5: Lorentz's velocity-dependent gravity explains the sense of Mercury's perihelion error (38", 32" left); accelerated planets radiate and fall into the Sun

I split this into three parts.

5a. Mercury and the Lorentz/Poincare gravity.

a. Mathematics. The essay gives no formula for the law [read: p.9-10]. The numbers in the Investigator's notes: Lorentz's 1900 law gave a Mercury change of 162 x 10^-10 per revolution (the Investigator's arithmetic from Lorentz's factors: about 1.4" per century); Lorentz concluded his modification "cannot account for the observed inequality" [web: https://en.wikisource.org/wiki/Considerations_on_Gravitation]. De Sitter (1911), for the Poincare/Minkowski-type relativistic gravity laws, found +7".15 per century for Mercury; Wacker 7".2; Lorentz in 1910 quoted 6".69 (a first approximation) [web: https://en.wikisource.org/wiki/On_the_bearing_of_the_Principle_of_Relativity_on_Gravitational_Astronomy]. Poincare's "6"" at Lille [web: fr.wikisource] fits those figures. So the essay's arithmetic is consistent with independent calculations of the same family of laws, provided the unit is per century. Note the three different "Lorentz laws" (1.4", 6".69, 7".15). The essay's "Lorentz's law" is not one fixed formula. Check of the shortfall: 6/38 = 16%; 32/38 = 84% unexplained (my arithmetic).

b. Experiments. The observed anomalous Mercury precession is 43"/century (Newcomb 1882, replacing Le Verrier's 38") and general relativity (GR) predicts 42.98"/century, which I confirmed by calculation: 6 pi G M / (c^2 a (1 - e^2)) per orbit with a = 5.791e10 m, e = 0.2056 and 87.969 days per orbit gives 42.99"/century [web: https://en.wikipedia.org/wiki/Tests_of_general_relativity gives the observed total 574.10 +/- 0.65"/century and GR 42.9799"/century]. Poincare's 38" is the Le Verrier value. The law the essay discusses supplies about 6-7" of about 43", so it explains about one sixth. The essay itself says it "does not suffice" [read: p.10]. Poincare's own claim is accurately modest: "the sense" (direction) is right, and the result is "hardly decisive". The direction is right (a positive addition). That is a fair, honest statement; it is not a claim of success.

c. Tested. Astronomically, yes: de Sitter computed it in 1911 and found the shortfall persisted; GR (1915) later accounted for the full excess [web: Wikipedia, Tests of GR]. The Lorentz/Poincare/Minkowski relativistic gravity laws were not further developed because of this and because of GR [memory, medium: the general history; not web-checked]. Replication: the 7" figure was replicated by Wacker, de Sitter, and (approximately) Lorentz, as calculations, not as experiments.

d. If true: GR's explanation of Mercury would be a coincidence, and gravity would be a Lorentz-invariant field in flat space with an unexplained 84% of the perihelion left. Not credible.

Verdict (5a): Tested, not supported as an explanation of Mercury (it accounts for about 6-7" of about 43" per century; the essay says as much). Historically superseded but instructive as a first attempt at relativistic gravity. The 38" and 32" per century reading is an inference supported by outside sources.

5b. Poincare-Lorentz gravity propagates at c, and Laplace's objection is dismissed. The Lille text gives Poincare's reply to Laplace's "ten million times c" limit: the result rested on a force direction like aberration and "ne prouve rien contre la theorie de Lorentz" [web: fr.wikisource]. This is a real physics point. For a finite propagation speed of gravity, a naive retarded Newtonian force gives a torque that would make orbits unstable, as Laplace argued, unless the velocity-dependent terms cancel it (as they do in GR; this is in effect what Poincare's "mainly compensated" says in his 1906 memoir [web, research notes]). Observation (binary pulsars, LIGO/GW170817) now shows gravity travels at c to about 1 part in 10^15 [memory, medium: not web-checked; not needed for the verdict since the essay does not rely on it]. So Poincare's reply is physically right in spirit. Verdict (5b): Plausible, untested as of 1909; Historically superseded but instructive.

5c. Planets radiate energy and spiral into the Sun in "millions of milliards of centuries" [read: p.9]. The reasoning: accelerated charges radiate, so accelerated celestial bodies do. This is correct only for electrically charged bodies. The Sun and planets are neutral to a high degree [memory, high], so there is no electromagnetic radiation of this kind. Gravitational radiation does exist in GR, but the essay is pre-GR. My calculation with the standard quadrupole formula: Earth about 196 W, Mercury about 69 W; inspiral time about 1e23 years for the Earth (about 1e21 centuries) (my calculation: P = 32/5 G^4 (M m)^2 (M+m)/(c^5 a^5); T = 5/256 c^5 a^4/(G^3 M m (M+m))). Poincare's "some millions of milliards of centuries" is 1e6 x 1e9 = 1e15 centuries, which is 1e18 years. His number is six orders of magnitude too small compared with the real gravitational-wave value of about 1e21 centuries, and for the wrong reason (charge radiation). As a physical claim: electromagnetic radiation from neutral planets: refuted by calculation (neutral bodies do not radiate). Gravitational radiation of planets: real, negligible, and it appears in the later theory. The 1909 essay does not mention gravity waves; I note this as the point where Poincare's reasoning happened to anticipate a real effect via a wrong mechanism (a Lorentz-invariant gravity theory would have gravitational waves; Poincare did propose "ondes gravifiques" in 1905 [memory, medium; not web-checked and not relied on]).

d. For all of claim 5 together: if the velocity-dependent Lorentz/Poincare gravity were the correct theory of gravity, GR, light bending at twice the Newtonian value, and the full Mercury precession would have to be coincidences of GR rather than consequences of curved spacetime.

Verdict (overall claim 5): split. Mercury explanation: Tested, not supported. Finite-speed gravity reply to Laplace: Plausible, untested as of 1909, historically superseded. Planetary spiral by EM radiation: Refuted by calculation (neutral bodies do not radiate electromagnetically; the real gravitational-wave decay is vastly slower, about 1e21 centuries for the Earth).

Claim 6: Newtonian mechanics is not finally condemned; it remains the mechanics of small velocities

a. Mathematics. For v much less than c, gamma = 1 + v^2/2c^2 + ...; at the Earth's orbital speed gamma - 1 = 4.9e-9 (claim 3 arithmetic); at Mercury's speed (47.9 km/s) about 1.3e-8 (my arithmetic: (47.9e3/2.998e8)^2/2). So Newton's laws are accurate to better than a part in 10^7 for everything in "practical life" [read: p.10]. Internally consistent: this is the correspondence principle.

b. Experiments. Consistent with all engineering practice; satellite navigation (GPS) needs relativistic corrections at the level of microseconds per day, precisely because clocks reach 1e-10 [memory, high; the numbers are not relied on]. The essay's warning about a "pedagogic danger" in French teaching is a sociological statement, not physics, which I note without judging [read: p.10-11].

c. Tested. Newtonian mechanics is the low-speed limit of SR and GR, confirmed by every precision test of the latter.

d. If true: nothing changes; this is mainstream.

Verdict: Established.

Investigator's findings: what I kept and how they bear

(All are kept in the record whatever the verdict. They are leads, which I weighed.)

1. The lecture is the Gottingen text (28 April 1909; Monist 1913). Weight: settles the date. It also means the essay is posthumous in English, translated by Halsted, and may omit material that was in the French. This matters for claim 5: the Lille text states the 6" outright, and names Bucherer and Kaufmann, where the Gottingen/Monist text does not. I could not find out whether the Gottingen French in Sechs Vortrage had these passages (the Investigator did not reach that volume). So I treat the missing 6" as unresolved.
2. Lille lecture (3 August 1909): the 6" figure; Bucherer named; inertial mass versus gravitational mass left undecided ("aucun moyen de decider"), which is the equivalence principle question; the Franklin-type charge-asymmetry origin of gravity (Lorentz); Laplace rebutted; the aberration test; planetary radiation sized at "a billion times smaller" than at a Crookes tube anticathode [web: fr.wikisource]. These show Poincare treated several points as open, not as claims of fact. The "Franklin" gravity as an unequal attraction between opposite charges is a mainstream-dismissed idea (it is refuted by calculation: the asymmetry needed is far below any measurement limit and would give a gravity law that does not satisfy the equivalence of inertial and gravitational mass to 1e-13 [memory, medium; not web-checked]). Weighed: it is Poincare's report of Lorentz's idea, not his own claim.
3. 1905/06 Palermo memoir: the mathematics, the Poincare stress, the "mainly compensated" gravity propagation. Weight: it is Poincare's technical statement. It shows (i) that he calls the relativity postulate testable; (ii) that his electron model needs a non-electromagnetic force, contradicting the essay's "only the ether is inert".
4. De Sitter 1911, Wacker, Lorentz 1910: independent calculations of 6.7-7.2"/century. Weight: corroborates the sizing of claim 5a; also shows the law was a modest fraction of the observed anomaly.
5. Bucherer 1908 and Bestelmeyer's, Minkowski's remarks; Kaufmann's own anti-relativity reading. Weight: the experimental basis of claims 1 and 4 was contested at the time; Poincare's essay presents it as settled. I keep both uses of Kaufmann.
6. Lorentz 1900: his own result was about 1.4"/century and "cannot account for the observed inequality". Weight: Poincare's essay credits Lorentz's law with explaining "the sense" of the error; Lorentz himself said it did not account for it. These are different figures from different versions of the law; I do not read this as an error by Poincare.
7. Truman State offprint "approximately 1902": unresolved; recorded only. Not physics.
8. Reception: a 1913 French review notice and a Dial notice (not opened); a geocentrist book citing the essay's relativity remark. The essay's remark that the Sun turning round the Earth is a convention is not a geocentric claim; at Lille Poincare rejected that reading ("je n'ai jamais eu une telle pensee") [web: fr.wikisource]. A modern use of an essay by a party with a stake in geocentrism is reported as that author's characterization.
9. Absence of evidence: the record is not silent on the project itself. The Investigator found no letters between Poincare and Halsted, Kaufmann or Bucherer in the Henri Poincare Papers calendar; the letter texts were not opened [web, research notes]. This is a gap in the search, not evidence about the claims.
10. Not reached (time limit): Sechs Vortrage 1910, Revue scientifique 1909, Lorentz Phys. Z. 1910, Wacker, HSNS 2023, Walter. Several bear on claims 1, 4 and 5; I list them as the records that would settle the open points (the Gottingen French, the data-quality study).

Summary table

Calculations (Python, my own): v^2/2c^2 for the Earth = 4.934e-9 (1/2.03e8); GR Mercury 42.99"/century; gravitational-wave power Earth 196 W, Mercury 69 W; inspiral time 1.07e23 yr (Earth); Mercury speed 47.87 km/s; gamma at 0.3178 c = 1.055 and at 0.6879 c = 1.378.

Web checks done (3): Mercury 38"/43" and GR 42.98" [https://en.wikipedia.org/wiki/Tests_of_general_relativity]; modern limits on Lorentz-invariance tests [https://en.wikipedia.org/wiki/Tests_of_special_relativity]; all other web material is from the Investigator's notes (not re-opened by me), tagged accordingly. Statements tagged [memory, medium] were not relied on for a verdict.