REVIEW 2 major objections 7 minor 5 references
En busca de los efectos gravitacionales de Birkhoff: la ultracentr{\i}fuga transelastica
T0 review · 2 major / 7 minor · reviewed 2026-08-14 · deepseek-v4-flash
Pith's one-line read A trans-elastic ultracentrifuge built to test a flat-space gravity theory did not confirm that theory but did demonstrate small, occasional solid-state uranium enrichment before the project was cancelled.
desk verdict A well-sourced history of a Mexican ultracentrifuge project; the physics-history sections are solid, but the uranium-enrichment claim is oversold and rests on a small, unreplicated SIMS subset. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the trans-elastic ultracentrifuge: a magnetically levitated, vacuum-enclosed steel-sphere rotor, up to 8 inches across, spun so fast that centrifugal forces exceeded the steel's elastic limit, producing plastic deformation or explosive failure. Its companion measurement and analysis chain is the key to both claims: real-time frequency monitoring with milliohertz precision for the spin-down test, and secondary-ion mass spectrometry with autoradiography to map uranium isotopes through the rotor. The theoretical motor is the predicted spin-down rate $$ \$\Delta$ = \frac{1}{f}\frac{df}{dt} = -\frac12 k\left(\frac{a\omega}{c}\right)^3\omega, $$ with $k=75\pi/128$ for a spherical rotor; the paper uses this formula to confront the flat-space theory with pulsar timing. The enrichment mechanism identified is forced diffusion of uranium atoms along the steel's grain boundaries, not bulk atomic diffusion through a fixed medium as originally assumed.
What would settle it
Re-analyze archived or newly cut slices from un-centrifuged control rotors with the same uranium insert geometry, prepared through the same thermal and analytical procedures, and compare isotope-ratio profiles with centrifuged rotors. If the order-of-magnitude $^{235}\mathrm{U}/^{238}\mathrm{U}$ excursions near the insert or rim also appear in controls, the enrichment claim is an artifact. Alternatively, a direct depth-resolved measurement with a method independent of secondary-ion mass spectrometry, such as resonant ionization mass spectrometry, on a new rotor run at known speed and temperature would settle whether enrichment is reproducible under controlled conditions.
Extended reading notes
Core claim
The paper's central claim is retrospective and double-sided. The prediction that a freely spinning steel sphere should lose angular momentum at a rate proportional to the fourth power of its rotation frequency, as a reaction from the flat-space gravity theory's interaction with the surrounding universe, is contradicted by astronomical timing of a 33-millisecond pulsar: the observed decay is orders of magnitude smaller than the predicted value, and the theoretical basis of the prediction was independently criticized as an incorrect treatment of self-interaction. Separately, the paper claims that the same centrifugation technology, operating into the plastic-deformation regime of its steel rotors, did produce local enrichment of uranium-235 relative to uranium-238 at rotor edges and near the uranium insert, as measured by an external laboratory on 56 samples from 14 rotors, but in only 15 percent of the analyzed slices and in small quantities. The final assessment is that solid-state centrifugal enrichment is possible in principle and demonstratively achieved locally, yet the project stopped at an embryonic stage without scalable protocols.
Load-bearing premise
The claim that solid-state centrifugation enriched uranium rests on a single external round of measurements; if those isotope-ratio readings were artifacts of sample preparation or the measuring technique, the positive enrichment result collapses.
Editorial extensions
If this is right
- If the enrichment result is taken as real, any future solid-state centrifugation effort must treat grain-boundary channeling as the controlling transport path, so rotor microstructure rather than spin alone determines where and whether enrichment occurs.
- The failure of the predicted spin-down effect under pulsar timing means that a flat-space gravity theory of this type cannot be validated by fast rotating bodies; any revival would need a different observable.
- The small, occasional nature of the enrichment, together with non-repetitive internal measurements, explains why the project was not deemed reliable enough to scale and was cancelled in 1986.
- The dual mission of the same instrument shows that tests of speculative gravity theories and practical isotope separation are not necessarily competing; here one machine served both, but design choices that served the gravity test (hard rotors, stable moment of inertia) conflicted with the enrichment goal (soft rotors with more grain boundaries).
Reading between the lines
- A controlled parametric extension would be to centrifuge identical uranium-loaded rotors for systematically varied durations, temperatures, and tip speeds and analyze grain-boundary isotope profiles, to see whether the local $^{235}\mathrm{U}/^{238}\mathrm{U}$ jump scales with strain rate rather than total spin time.
- The same pulsar null test can be applied to any future theory that predicts radiative spin-down of compact rotors scaling faster than standard general-relativistic quadrupole radiation; the crab-pulsar spin-down bound is a ready-made falsifier for such predictions.
- The observed pattern of enrichment at rotor edges and near the uranium-steel interface suggests that a practical process might exploit layered composite rotors rather than solid spheres with a single insert.
- The historical pairing of a gravity test with a uranium-enrichment mission suggests that political and funding context may have shaped technical choices; readers of the record should weigh that context when interpreting the scientific results.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. This paper reconstructs the history of the transelastic ultracentrifuge project at Mexico's Nuclear Center (1971-1986), from its origins in George Birkhoff's flat-space gravity theory and James Keith's predicted rotational drag effect, through the design and construction of the centrifuge, to its use for solid-state uranium enrichment. The manuscript argues that Keith's predicted effect is contradicted by pulsar observations and by Frehland's theoretical critique, and that the centrifuge produced small and occasional enrichments of 235U, based on a 1985 analysis of 56 samples from 14 rotors by Charles Evans & Associates. The paper is written as a historical narrative in Spanish with an English abstract.
Significance. If the historical claims were fully sustained, the paper would be a valuable contribution to the history of physics in Mexico, documenting a little-known episode connecting a heterodox gravity theory, the construction of an award-winning scientific instrument, and a nuclear-enrichment attempt. The reconstruction of the Birkhoff-Graef-Barajas theoretical program is well documented with archival references and citations, and the account of the pulsar and Frehland disproof of Keith's effect is clearly presented. The central weakness is the uranium-enrichment conclusion: it rests on a single external SIMS analysis with no reported controls, calibration standards, or independent replication, and the manuscript's own narrative records earlier non-reproducible data. The paper should be revised to align the strength of its empirical claim with the presented evidence.
major comments (2)
- [Section 9 and Section 10 (final comments)] The paper's conclusion that the ultracentrifuge 'permitió demostrar que es posible enriquecer uranio' overstates the evidence reported in Section 9. Of the 56 samples from 14 rotors analyzed by Charles Evans & Associates, 4 rotors showed no separation and only 15% of slices from 8 rotors exhibited notable 235U enrichment. No control rotors, unspun reference samples, or independent mass-spectrometric replication are described. This is particularly telling because the manuscript itself states that earlier internal SIMS results were non-repetitive and unreliable, with 1.5 dalton resolution and unresolved molecular interferences. The verb 'demostrar' should be replaced by a more cautious formulation such as 'sugieren' or 'apuntan a' unless further archival evidence is supplied.
- [Section 9, Fig. 7] The key evidence for enrichment is presented in Figure 7 as counts per second, described as 'directly proportional' to isotopic abundance, rather than as calibrated 235U/238U ratios. The most striking feature, an apparent order-of-magnitude 235U excess, is confined to a band of less than 0.25 micrometers adjacent to the uranium insert. That geometry is especially susceptible to SIMS artifacts at a metal/metal interface, including ion-beam mixing, crater-edge effects, and matrix-dependent ionization yields. The paper should either report the calibration standards and analytical controls used by the Evans laboratory, or add an explicit limitation statement warning the reader against interpreting the uncalibrated profile as proof of isotopic separation.
minor comments (7)
- [Abstract and Section 10] The abstract says 'Highly enriched uranium was obtained, but in small quantities,' whereas Section 10 says the quantities were 'pequeños y ocasionales.' The abstract should include the qualifier 'occasional' and ideally the more cautious framing that the evidence is suggestive rather than definitive.
- [Section 5 references to Carlos Graef] The text twice writes 'Cralos Graef' where 'Carlos Graef' is intended; please correct the typos.
- [Section 3] The name 'Birkhoff' is misspelled as 'Birkohff' in the paragraph describing the Cambridge gatherings; please correct.
- [Section 1 and footnote 2] The introduction states the project received the 'Premio Nacional de Ciencias 1973,' while the abstract and footnote 2 refer to the 'Premio Nacional de Instrumentación'; these should be reconciled.
- [Figure 7 caption] The caption should state whether the ordinates are raw counts or ratio-normalized to a standard, and should mark the natural 235U/238U ratio (approximately 0.0072) as a reference line so the reader can judge the magnitude of the excursions.
- [Throughout] The spelling of the surname 'Fremerey' varies among 'Fremerey,' 'Fremer ey,' and 'Femerey'; please standardize to the form used in the references.
- [Section 10, last paragraph] The two international publications cited (refs. 69 and 70) are mentioned but not summarized; adding a sentence on their reported content would help the reader assess the strength of the enrichment claim.
Circularity Check
Historical narrative with no derivation chain; the empirical claims rest on external measurements and prior literature, not on self-referential inputs.
full rationale
The paper is a historical review, not a theoretical derivation, so the circularity burden is low. Keith's decay formula is reported from his 1963 publication and is then tested against independent pulsar observations and Frehland's critique, external checks rather than the paper's own assumptions. The uranium-enrichment claim is based on the 1985 Charles Evans & Associates SIMS analysis performed by an outside company, not on a parameter fitted inside this paper. The earlier internal SIMS results are explicitly described as non-repetitive and not trusted by management, so the paper does not disguise those internal data as an independent confirmation. The final conclusion is an interpretation of external measurements, with the paper itself adding the limitations that the enriched volumes were small and occasional and that only 15% of slices from 8 of 14 rotors showed notable enrichment. While those limitations raise legitimate questions about evidence quality, they are not circularity. The only self-referential elements are historical testimonials and an internal project report cited for context about the project's origins and inspiration; those are not load-bearing for the main empirical claims. No equation is defined in terms of the quantity it is said to predict, no fitted value is renamed as a prediction, and no uniqueness theorem is imported from the authors' own prior work. The finding is therefore no significant circularity.
Assumptions & free parameters
assumptions (4)
- domain assumption The internal ININ reports and Keith's testimony accurately describe the project's goals and outcomes.
- domain assumption The 1985 Charles Evans & Associates SIMS analysis reliably measures uranium isotope ratios in the rotor samples.
- domain assumption Keith's 1963 rotational-decay formula is correctly transcribed from the original publication.
- ad hoc to paper The local 235U excesses measured by Evans represent genuine isotopic separation rather than SIMS artifacts or contamination.
Cite this review
Pith. "Pith review of En busca de los efectos gravitacionales de Birkhoff: la ultracentr{\i}fuga transelastica." pith.science (2026). https://pith.science/paper/2E4J7W3L
@misc{pith2026190804343,
author = {Pith},
title = {Pith review of: En busca de los efectos gravitacionales de Birkhoff: la ultracentr\ifuga transelastica},
year = {2026},
howpublished = {\url{https://pith.science/paper/2E4J7W3L}},
note = {Machine review of arXiv:1908.04343}
}
read the original abstract
This work reviews the origin, development, completion, and outcome of a trans-elastic ultracentrifuge project of Mexico's Nuclear Center through 1971 to 1986. The project had its origin in the search for an effect that supposedly would validate Birkhoff's gravity theory over Einstein's General Relativity. For this purpose an extraordinary ultracentrifuge was built which deserved the 1973 National Award for Instruments (Mexico). The ultracentrifuge was also used to investigate the feasibility of uranium enrichment by solid state centrifugation. Highly enriched uranium was obtained, but in small quantities.
Reference graph
Works this paper leans on
-
[1]
Introducción. La ejecución de grandes proyectos de investigación en Física experimental es un hecho relativamente reciente en México. Estos acontecimientos tuvieron que esperar la institucionalización de las ciencias físicas en nuestro país, misma que se dio ya muy entrado el siglo XX. Cabe recordar que no fue sino hasta el año de 1935 que se funda la aho...
work page 1935
-
[2]
La política de la buena vecindad. El sábado 4 de marzo de 1933, en la capital de los Estados Unidos, Franklin Delano Roosevelt pronunció ante su nación el discurso de toma de posesión a la presidencia. En él decía: “En el terreno de la política mundial, estableceré en esta nación la política del buen vecino –aquel que tenazmente se respeta a sí mismo, y a...
work page 1933
-
[3]
Las tertulias de Cambridge, Massachusetts. Hacia fines de 1941 en la ciudad de Cambridge, Massachusetts, se reunían informalmente un grupo de académicos de esa localidad, animados por la nueva política de “buena vecindad”. Entre ellos se encontraban, los matemáticos Norbert Wiener de MIT, George D. Birkohff de Harvard, el astrónomo Harlow Shapley del Obse...
work page 1968
-
[4]
tal y como Jimmy lo predecía, la frecuencia del rotor de su centrífuga debería ser observada con confiabilidad por al menos durante “un par de días” para poderla diferenciar de los otros efectos, cosa que su sistema no lo conseguía. En sus propias palabras, “La fiabilidad [de mi centrífuga] deberá ser incrementada hasta tener una estabilidad que dure “un ...
work page 1982
-
[5]
El flujo del uranio a través de la esf era de acero resulta del movimiento átomos individuales
a partir de cuyo perfil circular se distingue el flujo de uranio difundi do a través de las fronteras de grano (líneas zigzagueantes en la izquierda de la figura). 21 Figura 6 Auto-radiografía del corte transversal de un rotor centrifugado. A la derecha se distingue parte de la sección transversal del inserto cilíndrico de uranio (región más clara) cuyo r...
work page 1991
Reviewed August 14, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.