Hilgenberg-OC: Physicist review (Step 2)

Reviewer: PhD physicist. Tags: [read] document or Investigator's note, [web] with URL, [memory] with confidence, [calculation] my arithmetic (inputs listed).

Source gap (repeated from claims.md). The folder holds only Scalera and Braun (2003), a secondary summary by Earth-expansion proponents (interested parties). Hilgenberg's own gravity papers, Magnus reports, the 1939 flow booklet, the 1965 Geol. Rundschau paper and the 1974 monograph are not in the folder. The Investigator found his 1933 book Vom wachsenden Erdball online (archive.org) and read part of it; I did not re-read it myself, so that material is [read: Investigator note] at second hand. Where a conclusion below rests on Hilgenberg's own text only through those notes, I say so. Nothing here rests on [memory] alone for a verdict, but all numerical comparisons use my own numbers for present Earth (R = 6371 km, M = 5.97e24 kg, mean density 5.51 g/cm3 [memory, high]).

Corrections to Step 1

1. Claim 3 says 60%, 4590 km and 4 mm/yr "do not agree with each other as printed". Step 1 is right that they disagree, and the Investigator explains the 60%: in the 1933 book it is a diameter ratio of the shelf-fitting sphere (0.62-0.65), not a Permian radius [read: Investigator note, archive.org scan n20-n21]. I add a second reconciliation by calculation. The 1933 growth rate mu = 5.1e-17 per second (per unit mass) applied now gives dR/dt = R*mu/3 = 3.4 mm/yr, close to the 4 mm/yr figure. So 4 mm/yr is consistent with the 1933 exponential law. But the same mu over 250 Myr gives a Permian radius of 5570 km, not 4590 km. To reach 4590 km (0.720 R, mass ratio 0.374) in 250 Myr the rate must be 1.25e-16 per second, which makes the present rate 8.4 mm/yr. So the 4590 km map and the 4 mm/yr caption cannot both come from one exponential law with one rate. (The 1965 paper may use a different age or law; unread.) [calculation]
2. Step 1's deep read lists the 1933 report as "most plausibly" Magnus-inversion work. That remains inference. Hilgenberg's own booklets (1931 pp.14-15, 1939) are where the sink/source experiments are; none was read by any step.
3. Step 1 says the folder document presents the ether-gravity mechanism "favourably". True, but the document gives no equation. Claim 1 therefore cannot be judged on mathematics from the folder alone. I use the Investigator's reading of the 1933 text (no equations either: a verbal sink/stream picture).
4. Dating slip in the document (CMB "1968") is the authors'; the discovery is 1964-65 [memory, high]. Immaterial to verdicts.

Mainstream view, stated fairly

Gravity: Newtonian inverse-square law and general relativity (GR; gravity as spacetime curvature), tested to high precision in the solar system. Earth's radius: plate tectonics (rigid plates moving on a sphere of constant radius, new ocean floor made at ridges and destroyed at subduction zones) explains the ocean floor, magnetic stripes, Benioff seismic zones and slab images from seismic tomography. Expansion was a respectable minority hypothesis in the 1960s-70s (Carey, Egyed, Hilgenberg) and was later tested and rejected by paleomagnetic and space-geodetic constraints. I state the physics verdict below; I keep the expansion community's evidence and Hilgenberg's own arguments in the record.

Claim 1. Gravity is the accelerated flow of space (ether) into masses acting as sinks

a. Mathematics. No equations in the folder or in the 1933 passages read. I tested the idea on its own terms. A point sink in an incompressible fluid has speed v = Q/(4 pi r^2). The acceleration of a fluid element is v dv/dr, which falls as r^-5, not the observed r^-2. To get g = GM/r^2 the flow must follow v = sqrt(2GM/r) (the free-fall speed), which falls as r^-1/2 and so is not incompressible (continuity needs density to rise as r^-3/2 toward the body, or matter to be absorbed along the path). So a literal "point sink in an ordinary fluid" gives the wrong force law; a specially chosen flow gives the right one. Hilgenberg's text as reported gives no such law. Also, the verbal rules (like sinks attract, sink and source repel [read: Investigator note]) are the old hydrodynamic analogy of the Bjerknes pulsating-sphere experiments [memory, medium: this is the Investigator's lead and I did not verify it]; they match Newtonian signs for sinks but the analogy is known to give the force of the inverse-square form only for pulsating spheres in an ideal fluid, with the sign of attraction reversed relative to in-phase pulsation. Verdict on internal consistency: undetermined from the text, underspecified; the stated sink picture needs a flow law that is not given. b. Experiment. The flow picture would be indistinguishable from Newton/GR if tuned to v = sqrt(2GM/r). The rigorous version of this exists: the "river model" of the Schwarzschild solution, in Painleve-Gullstrand coordinates, where space flows inward at the escape velocity and reaches light speed at the horizon [web: https://arxiv.org/abs/gr-qc/0411060, Hamilton and Lisle]. This supports a real mathematical analogy (and the folder's claim 6 black-hole remark) but it is a re-description of curved spacetime in which nothing is converted into matter and nothing is absorbed. The additional content of Hilgenberg's version, that ether is consumed, is tested under claim 2. c. Tests. The sink/stream effects were shown in water or air tank experiments by Hilgenberg (1931, 1939) and, earlier, Westphal [read: Investigator note]. Those demonstrate fluid analogies, not gravity. No test of the ether itself exists; the Michelson-Morley null result and later modern bounds on a preferred frame (not looked up here) constrain a stationary ether; a flowing ether tied to each mass would need separate treatment which Hilgenberg does not give. Dayton Miller's drift claim, used by Hilgenberg early, was judged flawed even by the folder authors [read: p.7]. d. If true: GR's equivalence principle and the Newtonian inverse square law would need a derivation from fluid mechanics; a preferred ether frame would conflict with special relativity, which Hilgenberg rejected early and accepted with reservations by 1974 [read: p.7]. Related work kept in the record: Riemann (1853 ether-sink idea, which Hilgenberg himself names as independent parallel [read: Investigator note]), Yarkovsky 1888 (ether inflow into bodies and conversion to matter) [Investigator, naturalphilosophy wiki], Le Sage/Fatio push gravity, Krafft's vortex ether, Scalera 2021 [Investigator]. These are the same family of ideas; the Investigator's labels such as "false" in the sources are those sources' characterizations. Verdict: Not testable as stated (strong form: ether is a distinct material fluid with different observable consequences from GR). Plausible, untested only for the weak form: gravity can be written as a flow of space (river model), which is mathematics equivalent to GR for static masses, not a new theory.

Claim 2. Inflowing ether is converted inside planets into new matter; Earth's mass grows exponentially

a. Mathematics. The 1933 growth law as read: M'/M = exp(mu t), M/M' = 0.6^3 = 0.216, t = 1 Gyr = 3e16 s, mu = ln(4.63)/3e16 = 5.1e-17 per second; "15 million new molecules per second per gram of hydrogen" [read: Investigator note]. I verified both numbers [calculation: ln 4.63 = 1.532; 3.0e23 molecules per gram x 5e-17 = 1.5e7]. Internally consistent. The unit printed "g/sec" is a typo for per second (the Investigator's note). The assumption of constant density is stated by Hilgenberg as simplifying and untrue. Note an inconsistency with claim 3 (see Corrections). b. Consistency with measurement. With the 4 mm/yr figure at constant density 5514 kg/m3: mass gain 3.6e8 kg/s (1.9e-9 of Earth's mass per year, i.e. 6e-17 per second). [calculation] - Energy: creating that mass needs 3.2e25 W of rest energy (3.6e8 kg x c^2), about 2e8 times the sunlight Earth intercepts (1.7e17 W [memory, high]). The ether is therefore a reservoir of enormous energy flux at the surface. Hilgenberg's own phrase, "slight energy density", is not compatible with this unless the flow is large, and if the ether moved at Earth's escape speed 11.2 km/s the required ether density at the surface would be 6e-11 kg/m3 (our same assumption). Neither number is derived by anyone; it is a consistency requirement, not evidence the idea is false in itself. - Orbit: mass added at rest relative to the Sun would carry no angular momentum; for a circular orbit with conserved angular momentum r scales as 1/m^2, so an Earth that gained mass would have orbited farther out, not closer, in the past, and the 1933 claim that orbits widen with mass growth goes the opposite way [calculation; depends on the unstated assumption that the new mass has no orbital momentum; Hilgenberg's own flow model might differ]. I flag this as a question the theory has to answer, not as a refutation. - Gravitational parameter: GM would rise 1.9e-9 per year. Satellite laser ranging and lunar laser ranging fix GM and the Earth-Moon distance very precisely, and Scalera et al. have a paper titled "Are artificial satellites orbits influenced by an expanding Earth?" [Investigator, Earth-Prints title only; not read]. I did not find or compute the limit; this is an open check for the Arbiter. c. Tests. Space geodesy limits the present radius change (see claim 3). No one has measured ether flow, matter creation, or a "swallowing constant". Hilgenberg's 1967 "swallowing constant" manuscript was unpublished and sent to Runcorn; value unknown [read: p.17]. Scalera (2021) attempts first estimates of ether density, velocity and flux and claims geoneutrino data corroborate; Scalera is an interested party and I did not read the PDF [Investigator, web: https://www.earth-prints.org/handle/2122/14738]. d. If true: conservation of mass-energy would have to hold with an external energy reservoir; baryon number conservation would be violated at about 3.6e8 kg/s (about 2e35 baryons per second [calculation: 3.6e8 / 1.67e-27]); the Standard Model would need a matter-from-vacuum process with no observed analogue. Verdict: Never properly tested for the existence of the conversion as such (no neutral experiment; the idea was rejected without a test: the thesis in 1937-38 and the 1974 open letter produced no recorded reply). Split: the specific form with mu about 5e-17 per s (4 mm/yr now) is Tested, not supported (claim 3).

Claim 3. Earth's radius has nearly doubled since the Paleozoic (60% of present; 4590 km Permian; 4 mm/yr)

a. Mathematics. Mutually inconsistent as printed (see Corrections 1). Additional numbers [calculation]: 4590/6371 = 0.720 (volume 0.374). "Nearly doubling" would be about 0.5. If the mass stays constant instead (the "no new matter" alternative the 1974 letter raises [read: p.13]), the mean density at 4590 km would be 14.7 g/cm3, higher than the present inner-core density (about 13 g/cm3 at much higher pressure [memory, medium]), which is not credible for a body with a rocky mantle. The arithmetic of the shelf-sphere fit itself (shelves are about 35% of surface; sqrt 0.35 = 0.59) is fine and the Investigator confirms that Hilgenberg shows this [read: Investigator note]. b. Experiment. (i) Paleomagnetic paleoradius: McElhinny, Taylor and Stevenson (1978) limit expansion over 400 Myr to less than 0.8% [web: https://www.nature.com/articles/271316a0.pdf]. Hilgenberg wants about 28% shrinkage by the Permian. (ii) Space geodesy (SLR, VLBI, GPS, DORIS and GRACE) finds the radius change consistent with zero, 0.1 +/- 0.2 mm/yr [web: Wu et al. 2011, summarised at https://www.sciencedaily.com/releases/2011/08/110817120527.htm]. A value of 4 mm/yr is 20 times that uncertainty. (iii) Ocean floor: the oldest in-place ocean crust is about 180 Myr; its ages and magnetic stripes fit spreading on a sphere of present radius [memory, high]. (iv) Day length: expansion with angular momentum conserved (I proportional to M R^2, so R^5 at constant density) makes the Permian day 4.7 hours [calculation: 24 x 0.72^5]; coral growth rings give about 400 days per year at about 400 Ma (about 21.9 h days) [web: https://scienceblog.com/t-coral-growth-rings-400-days-year/], and Hilgenberg predicted days shortening, the opposite of tidal slowing [read: Investigator note]. If angular momentum is not conserved, ether supplies it, but no mechanism is given. c. Tests. Geometric method: Hilgenberg's reconstructions on paper-on-globe constructions are checkable by the reader and were checked by advocates only. The globe workshops are advocates [read: Investigator note]. The paleomagnetic and geodetic tests above are by independent groups (Nature 1978; Wu et al. 2011). The expansion side's reply (e.g. Scalera, Maxlow) was not read; the claim that the 1978 test is weak because its data come from reconstructions made on fixed radius is an argument I have not been able to check from the folder. d. If true: plate tectonics' spreading and subduction balance, GPS plate motion sums, and the paleomagnetic record would all have to be wrong. Verdict: Tested, not supported (strong form: R about 0.72 at the Permian, or 4 mm/yr now). Weak form (some very small secular change, below 0.2 mm/yr): Never properly tested, consistent with measurement limits.

Claim 4. Ether flow to the Sun plus the "inverted Magnus effect" spins planets up until an equatorial ring detaches

a. Mathematics. No equations. The Magnus effect (lift on a spinning body in a crossflow) is real. The inverse (negative) Magnus effect is real too: it occurs in a narrow band of Reynolds number (about 1e5) at low spin ratio, because the boundary layer on the side moving against the flow turns turbulent first and separation moves downstream [web: https://cambridge.org/core/journals/journal-of-fluid-mechanics/article/inverse-magnus-effect-on-a-rotating-sphere-when-and-why/0E9FEF2880AA45C8B12587374C6F10EE and https://arxiv.org/pdf/2302.11260]. So Hilgenberg's laboratory effect has a legitimate hydrodynamic basis, though whether his 1933 report identifies the mechanism is unread. The step from a viscous boundary-layer effect at Re about 1e5 to a planet in an ether is not derived; there is no Reynolds number, no viscosity, no boundary layer for a planet in a radial flow. b. Experiment. Observed planetary spins: tidal friction drives bodies toward synchronous rotation and slows the Earth (a lengthening of the day of about 1.7 ms per century in the long run [memory, medium: not rechecked]); fossil day counts agree (claim 3b). No solar-system planet is near the rotation needed for ring expulsion; the folder's authors say this themselves ("less valid today") [read: page image p.10]. c. Tests. The 1933 effect was "completely proven" in the TH Berlin lab by Hilgenberg's own account [read: p.9]; no apparatus, data or witnesses are given. No replication on record; nothing on record shows the experiments were ever challenged either, since the lab results were not published beyond his own reports and Z. Techn. Phys. 14 (211-214) (unread). d. If true: planetary spin would be driven by ether flow, not by accretion history and tidal torque. Verdict: Split. Inverse Magnus effect as a lab fluid effect: Established (as independent literature shows; Hilgenberg's 1933 work not checked). Planetary spin-up and ring expulsion: Tested, not supported (observed spins, tidal evolution, fossil day counts; the folder authors concur).

Claim 5. Reconstructions on smaller globes with paleopoles give a consistent paleogeography and explain trenches, rifts and Benioff zones without subduction

a. Mathematics. The globe-transposition geometry (equidistant azimuthal projection, removing radial slices [read: p.11]) is a legitimate construction. Internally consistent; paleopole handling at variable radius is the authors' claim, not checked. b. Experiment. Authors concede the Pacific solution is "not in agreement with the most up-to-date paleomagnetic data" [read: p.11]. Hilgenberg's Benioff zones as rising dunite are contradicted by tomography showing cold slabs to about 700 km and beyond (mainstream) and earthquake focal mechanisms; the folder authors say only that it "might once again be appraised" [read: p.11-12]. A 1962-66 body of paleomagnetic work was available to Hilgenberg; it did not include the later oceanic magnetic anomaly record. c. Tests. Reproduced by the globe workshops (advocates). Critics at TU Berlin and Darmstadt (2001): Bruhn (subduction shown by tomography, mass conservation), Seiler ("gut-feeling"), Thorweihe (no expansion discussion in modern geoscience) [read: Investigator note; these named critics are the closest to an expert reply]. Note the flaw in the framing: Fiedler-Volmer, Oppermann and TU geology professors Quiring and Zeil (supporters, workroom provided) show that he was not simply shut out by his institution [read: Investigator note]. d. If true: plate tectonics would need replacing by expansion at about 0.6 million km2 per year of new surface [calculation at 4 mm/yr] with subduction absent. Verdict: Tested, not supported (the Pacific reconstruction and no-subduction claims; ocean-floor, tomography and paleoradius evidence above). Plausible, untested for the narrower geometric claim that some Carboniferous-Tertiary continental outlines can be fitted on a smaller globe (fitting is underconstrained).

Claim 6. "Expansion with or without new matter"; ether picture analogous to GR; star with ether inflow at light speed is a black hole

a. Mathematics. The conversion Riemann-to-GR ("set the ether energy density to zero, add a fourth coordinate") is not shown [read: p.14]. The speed-of-light and black-hole parallel is valid in the river model: inflow speed equals c at the horizon [web: arxiv gr-qc/0411060]. That is a re-expression of Schwarzschild geometry, not a derivation of black holes from ether consumption. The authors' "equivalent in every way" is stronger than shown. b. Experiment. Black holes themselves are supported by observation (gravitational-wave mergers, stellar orbits at Sgr A) [memory, high], but no observation distinguishes the ether interpretation from GR. c. Tests. The 1974 open letter to Wilson, Beloussov and van Bemmelen: no reply reported [read: p.13-14]. The folder authors report none; whether any exists is unknown and not found by the Investigator (archival check not done). Hilgenberg compared ether flow with Riemann already in 1933 [read: Investigator note]. d. If true: nothing new would have to change in GR's predictions; only its interpretation. Verdict: Not testable as stated (interpretation with no measurable difference). The "no new matter" expansion option (Hilgenberg's own alternative, also Jordan/Dirac decreasing G, Herndon's decompression) is Tested, not supported for the Earth over 400 Myr (McElhinny et al. 1978 also limit G change: below 8e-12 per year [web: Nature link above]) and Refuted by calculation* at R = 0.72 with constant mass (mean density 14.7 g/cm3).

Historical record and Investigator's findings I keep

• Thesis rejection: three accounts (Scalera-Braun: committee; German Wikipedia: 1938, Faculty of Mechanical Engineering, over conflict with relativity; Thielmann 2015 and zillmer.com: 1937). None cites the faculty file; the TU Berlin Universitaetsarchiv record is the deciding record, not obtained. NSDAP refusal blocking a chair: three accounts, all from the same advocacy circle. I treat these as documented in several published secondary sources by interested parties and not independently corroborated, as the record stands. Physics verdicts do not depend on them.
• Wartime and postwar facts (Gatow books, Staatsbibliothek 1947-50 and dismissal) are biography; no bearing on the claims.
• Witnesses and critics (TU intern 2001-02), Yarkovsky 1888, Krafft, Scalera 2021, Herndon, Farrell's popular books (vortex-ring atom 1959 models: not read; no verdict) and the Met Office copy of the 1931 booklet are all retained above or as leads.
• Absence of evidence: the 1931 and 1939 booklets, the 1933 Magnus reports and the 1965 paper were never found in primary form by any step except the 1933 book; no experiment by anyone other than advocates; no reply from the 1974 addressees. Competing explanations: no one with standing replied because the work was seen as outdated by 1974 (plate tectonics consolidated by 1970s); replies exist but are unindexed; works not read by mainstream because self-published. The deciding records: faculty file, Geotekt. Forsch. 45 reception, letters in the Hilgenberg estate (held by his daughter Helge [read: p.11]).

Verdict summary

Web checks done (6 of 6 budget)

1. Wu et al. 2011 (sciencedaily/PNSN summaries). 2. McElhinny, Taylor, Stevenson 1978 (nature.com). 3. Hamilton and Lisle river model (arXiv). 4. Inverse Magnus effect (JFM, arXiv). 5. Coral growth rings (scienceblog). Not verified: lunar recession 3.8 cm/yr, long-term day lengthening, Bjerknes analogy, inner-core density, Riemann 1853: all [memory], medium confidence, none decisive for a verdict except the density figure (the verdict at R = 0.72 also holds against rock density alone).