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REVIEW 3 major objections 4 minor 55 references

New constraints on the values of the fundamental constants at a look-back time of 7.3 Gyr

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read New limits from hydroxyl absorption lines at z = 0.89 bound changes in the fine-structure constant, the proton-electron mass ratio, and the proton g-factor over 7.3 Gyr, all consistent with no evolution.

desk verdict A new but weak data point on alpha and g_p at z=0.89 that hangs on an unquantified conjugate-line assumption; fine as a null result, needs systematics before being used as a reference. read the letter →

arxiv 2505.07200 v2 pith:FYBFQ3XV submitted 2025-05-12 astro-ph.CO

Renzhi Su , Stephen J. Curran , Francoise Combes , Neeraj Gupta , Sebastien Muller , Di Li , Minfeng Gu This is my paper · ORCID
classification astro-ph.CO
keywords fundamentalconstantsfinestructureconstantprotong-factorOH18cmlinesconjugatesatelliteabsorptionspectroscopyPKS1830-211cosmologicalevolutionof
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that the fine-structure constant $\alpha$, the proton-electron mass ratio $\mu$, and the proton g-factor $g_p$ have not changed detectably over the past 7.3 billion years. The evidence comes from a re-analysis of the four hydroxyl (OH) 18 cm absorption lines toward the lensed quasar PKS 1830-211 at $z = 0.89$, where all four lines arise in the same gas and any frequency mismatch between them carries information about constant evolution. Combining a methanol-based prior of $\Delta\mu/\mu = (-1.8\pm1.2)\times10^{-7}$ with the fitted OH line offsets yields upper limits of $\Delta(\alpha g_p^{0.27})/(\alpha g_p^{0.27}) \lesssim 5.7\times10^{-5}$, $\Delta\alpha/\alpha \lesssim 2.3\times10^{-3}$, and $\Delta g_p/g_p \lesssim 7.9\times10^{-3}$. The result matters because unified theories predict slow drift in these constants, and radio absorption lines offer the cleanest astronomical probe over cosmological timescales.

What carries the argument

The load-bearing object is the frequency pattern of the four OH 18 cm lines. In the rest frame the frequencies satisfy $\nu_{1612} + \nu_{1720} = \nu_{1665} + \nu_{1667}$, and each transition has a different sensitivity coefficient to $\alpha$, $\mu$, and $g_p$. Because the lines come from the same gas, physical velocity offsets cancel; only differential shifts remain. The fitting procedure adds two free offsets, one between the 1665 and 1667 MHz lines and one between the 1612 and 1667 MHz lines, models the 1612/1720 pair as conjugate absorption/emission, and converts the fitted offsets into the linear equations that constrain the constant variations.

What would settle it

Fitting the same spectra while allowing the 1612 and 1720 MHz rest frequencies to float independently, or modeling the OH excitation with a radiative-transfer code that predicts an intrinsic $1612{-}1720$ offset at the $\sim 10^{-5}$ fractional level, would settle whether the conjugate assumption is safe; a still cleaner check is to observe a local ($z=0$) OH absorber with similar physical conditions and test whether the satellite lines are exactly conjugate when the constants are known to be unchanged.

Watch

Extended reading notes

Core claim

The central discovery is a null measurement of cosmological constant evolution in the $z = 0.8858$ absorber toward PKS 1830-211. By simultaneously fitting two thermalized OH main lines (1665 and 1667 MHz) and two conjugate OH satellite lines (1612 absorption and 1720 emission), the paper obtains two linear combinations relating $\Delta\mu/\mu$, $\Delta\alpha/\alpha$, and $\Delta g_p/g_p$. Substituting the prior $\Delta\mu/\mu = (-1.8\pm1.2)\times10^{-7}$ gives $\Delta(\alpha g_p^{0.27})/(\alpha g_p^{0.27}) = (-3.2\pm5.7)\times10^{-5}$, $\Delta\alpha/\alpha = (-3.3\pm23.0)\times10^{-4}$, and $\Delta g_p/g_p = (1.1\pm7.9)\times10^{-3}$, which the paper quotes as 1$\sigma$ upper limits $5.7\times10^{-5}$, $2.3\times10^{-3}$, and $7.9\times10^{-3}$. It concludes that the constants are consistent with no evolution over a look-back time of 7.3 Gyr.

Load-bearing premise

The result collapses if the four OH 18 cm lines do not trace exactly the same gas, or if excitation and radiative-transfer effects produce intrinsic frequency shifts between the 1612 and 1720 MHz satellite lines, because the fitting would then attribute those shifts to changes in the constants.

Editorial extensions

If this is right

  • If the limits are correct, any model predicting fractional changes larger than roughly $10^{-5}$ in $\alpha g_p^{0.27}$, $10^{-3}$ in $\alpha$, or $10^{-2}$ in $g_p$ by $z < 1$ is ruled out.
  • The measurement adds a second, independent constraint at $z = 0.89$ alongside the much tighter methanol-based $\mu$ bound, and it is one of the few direct bounds on $g_p$ evolution.
  • The null result extends constant-drift tests to a look-back time of 7.3 Gyr, beyond the reach of terrestrial atomic-clock and Oklo reactor limits.
  • With only one OH absorber known above $z = 0.1$, this is currently the highest-redshift anchor for simultaneous $\alpha$, $\mu$, and $g_p$ constraints from a single species.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: if a second OH 18 cm absorber is found at a different redshift, the same pipeline would turn this single null result into a two-epoch measurement, which is the minimum needed to separate a real drift from a constant systematic offset.
  • Editorial inference: the $g_p$ and $\alpha$ limits are dominated by the satellite-line frequency combination $\nu_{1720}-\nu_{1612}$, so deeper integrations on the 1720 MHz line alone could tighten both limits substantially without new instruments.
  • Editorial inference: the conjugate-line assumption is only validated statistically on noise-dominated residuals; a velocity-resolved comparison of the 1612/1720 line ratio against the fitted offsets would test whether an excitation effect is masquerading as a constant change.
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Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This paper re-analyzes the MeerKAT OH 18 cm absorption spectra toward PKS 1830–211 at z≈0.8858, fitting the four lines with a model consisting of two thermal (LTE) Gaussian components and two conjugate satellite components, with global frequency offsets FO1 and FO2 between the 1665/1612 lines and the 1667 line. Using the sensitivity equations of Chengalur & Kanekar (2003) and adopting the independent methanol-based Δμ/μ = (-1.8±1.2)×10^-7 (Muller et al. 2021), the authors derive Δ(αg_p^0.27)/(αg_p^0.27) = (-3.2±5.7)×10^-5, Δα/α = (-3.3±23.0)×10^-4, and Δg_p/g_p = (1.1±7.9)×10^-3, which they interpret as upper limits consistent with no evolution over 7.3 Gyr.

Significance. If the underlying assumptions hold, this is a useful new null measurement of fundamental-constant evolution at z=0.89, and one of the very few cosmological constraints on the proton g-factor. The use of same-species lines avoids inter-species velocity offsets, and the simultaneous fit with tied strengths and widths is a reasonable approach. The statistical checks (reduced χ²=1.17, KS and AD p-values of 0.64 and 0.46) are reported transparently, and the paper is honest about the key assumptions. The main value is as a new data point for the evolution of α and especially g_p, though the precision is modest compared to other probes of α.

major comments (3)
  1. [Section 3, conjugate-line assumption] The paper states that 'a crucial assumption is the existence of conjugate OH satellite lines,' but the KS and AD tests (p = 0.64 and 0.46) are performed on the summed residual after the conjugate-tied model is subtracted; they test whether that residual is consistent with Gaussian noise, not whether the data exclude a non-conjugate component of the size relevant here. A centroid offset of ~1–2 km/s between the 1612 and 1720 conjugate components (or between the 1665 and 1667 main-line components) would produce residual amplitudes of order A×Δv/FWHM ≈ 2×10^-5, below the per-channel rms of ~2×10^-4, so the test cannot bound such offsets. Since the derived limits on Δα/α and Δg_p/g_p in Eq. (5) correspond to frequency offsets of order 1–10 kHz (roughly 0.2–2 km/s), an excitation-induced offset of this size would shift the central values by an amount comparable to their stated uncertainties. The paper should either constrain the size of possible excitation-induced frequency offsets from OH radiative-transfer/excitation models, or add a systematic error term to the limits that accounts for this. As written, the quoted constraints in Eq. (5) and the Summary rest entirely on an assumption whose associated uncertainty is not bounded.
  2. [Section 4, Eq. (5)] The combination of Eqs. (1a),(2a) and (1b),(2b),(3),(4) uses inverse-variance weighting, which assumes the individual component measurements are statistically independent. However, G1–G4 are fitted simultaneously with global offsets FO1 and FO2, so the parameter estimates are correlated. Without the covariance matrix (or a justification of independence), the quoted uncertainties of 7.9×10^-3 and 2.1×10^-4 in Eq. (5) may be underestimated. Please propagate the full covariance of the fit into the combined constraints, or explain why the components can be treated as independent.
  3. [Section 3, Table 1] The fitted values and uncertainties of the global frequency offsets FO1 and FO2, which are the direct observables entering Eqs. (1)–(5), are not reported anywhere. The reader cannot verify the error propagation from the line centroids to the final constant limits. The paper should list FO1, FO2 (and their covariance), and state explicitly how the uncertainties on the right-hand sides of Eqs. (1)–(4) are derived from the fit.
minor comments (4)
  1. [Section 6] The reported '1σ limits' are actually the 1σ uncertainties of the fitted constants rather than upper limits computed from the full posterior: for Δg_p/g_p = (1.1±7.9)×10^-3, the 1σ upper limit is 9.0×10^-3, not 7.9×10^-3. Please clarify how the limits are defined and whether the central values are being included.
  2. [Section 4] The text refers to 'comparisons of the redshifts between ν1667+ν1665 and ν1667-ν1665,' but the equations appear to use frequency combinations with a different normalization. Please rewrite this sentence to match the actual equations and definitions used.
  3. [Figure 1 and Table 1] There are encoding artifacts in the displayed text (e.g., '/uni03BC/' and 'Normali ed flux den ity'), which should be fixed in the final version.
  4. [Abstract and Summary] The abstract quotes limits with the symbol '≲' but the body gives central values and uncertainties; please be consistent about whether the constraints are 1σ upper limits or 1σ uncertainties, and specify the confidence level (1σ, 2σ, etc.).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the OH frequency offsets are measured from the spectra and converted to fundamental-constant limits through published sensitivity coefficients and an external methanol-based Δμ/μ prior.

full rationale

The derivation chain is self-contained as a measurement: the paper first fits Gaussian components to the four OH 18 cm spectra and introduces free frequency offsets FO1 and FO2; it then converts the measured offset combinations into linear equations in Δμ/μ, Δα/α, and Δg_p/g_p using the published frequency-constant sensitivity relations (Chengalur & Kanekar 2003); finally it combines these with the independent methanol constraint Δμ/μ=(-1.8±1.2)×10^-7 (Muller et al. 2021) to solve for the two remaining constants. No step defines one target constant in terms of another, fits a parameter to a subset and then presents a closely related fitted quantity as a prediction, or imports a uniqueness result from the same authors. The Muller et al. prior comes from different molecular lines (CH3OH) and, although one author overlaps, it is an externally published measurement used transparently as an input rather than as an unverified self-citation. The 'crucial assumption' of conjugate OH satellite lines is a physical modeling choice with a statistical test (KS and AD p-values of 0.64 and 0.46); if wrong it could bias the derived limits, but that is a systematic-uncertainty concern, not a circular reduction. The paper also explicitly discusses the dominance of the ν1720−ν1612 and ν1667−ν1665 uncertainties and notes the ∼3.7σ residual feature, further indicating that the quoted limits are data-driven rather than forced by construction. No circular step is identifiable by the standards of this review.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central constraints are drawn from measured line centers plus the prior methanol mu value; no new entities are introduced. The main burden is the excitation/kinematic model for OH, specifically the same-gas and conjugate-line assumptions, and the adopted sensitivity coefficients from Chengalur and Kanekar (2003). The tight alpha g_p^0.27 limit is robust to the mu input but depends on the rest-frequency physics.

free parameters (3)
  • FO1 (1665-1667 frequency offset) = Not quoted directly; implied by Table 1 line centers (order kHz)
    Added to the expected 1665 MHz frequency in the 14-parameter simultaneous fit; its value drives the Delta g_p/Delta alpha decomposition through Eqs. (1a), (2a), and (5a).
  • FO2 (1612-1667 frequency offset) = Not quoted directly; implied by Table 1 line centers
    Added to the expected 1612 MHz frequency; it sets the 1720-1612 versus 1667+1665 comparison that yields the tight Delta(alpha g_p^0.27) constraint in Eqs. (1b)-(5b).
  • Input Delta mu/mu from methanol = (-1.8 +/- 1.2)e-7
    Adopted from Muller et al. (2021); substituting it into Eq. (5) separates Delta alpha/alpha from Delta g_p/g_p, though the alpha g_p^0.27 combination is nearly independent of this input.
assumptions (6)
  • domain assumption The OH 18 cm rest frequencies and the sensitivity coefficients in Eqs. (12)-(13) of Chengalur and Kanekar (2003) correctly map frequency offsets to Delta alpha/alpha, Delta mu/mu, and Delta g_p/g_p.
    Used unchanged in Section 4; no re-derivation or uncertainty estimate is provided for these coefficients.
  • domain assumption The four OH 18 cm lines originate from the same gas at the same redshift, so fitted offsets FO1 and FO2 are not caused by velocity differences between the lines.
    Section 3 fits all lines simultaneously under LTE; this is the central premise that turns inter-line frequency offsets into constant evolution.
  • domain assumption The 1612/1720 satellite lines are exactly conjugate, with residual noise symmetric after thermal subtraction.
    Tested with KS and AD tests (p=0.64 and 0.46) but assumed in the fit; a 3.7-sigma residual at 912.4 MHz is dismissed as a noise peak.
  • domain assumption The methanol Delta mu/mu measurement of Muller et al. (2021) is valid for the same absorbing gas and the proton-electron mass ratio did not vary between the methanol and OH regions.
    Used in Eq. (5) to break the degeneracy between Delta alpha/alpha and Delta g_p/g_p.
  • domain assumption The chosen Gaussian component structure, two main-line components plus two conjugate satellite pairs, is a complete description of the absorption.
    Section 3; reduced chi-squared of 1.17 supports it, but the weak third component seen by Combes et al. (2021) is omitted.
  • domain assumption Standard Lambda CDM cosmology with H0=70 km/s/Mpc, Omega_m=0.3, and Omega_Lambda=0.7 is sufficient for the 7.3 Gyr look-back time.
    Section 1; the look-back time is context, not an input to the constraint equations.

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Pith. "Pith review of New constraints on the values of the fundamental constants at a look-back time of 7.3 Gyr." pith.science (2026). https://pith.science/paper/FYBFQ3XV

@misc{pith2026250507200,
  author       = {Pith},
  title        = {Pith review of: New constraints on the values of the fundamental constants at a look-back time of 7.3 Gyr},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FYBFQ3XV}},
  note         = {Machine review of arXiv:2505.07200}
}
abstract

The study of redshifted spectral lines can provide a measure of the fundamental constants over large look-back times. Current grand unified theories predict an evolution in these constants and astronomical observations offer the only experimental measure of the values of the constants over large timescales. Of particular interest are the dimensionless constants: the fine structure constant ($\alpha$), the proton-electron mass ratio ($\mu$), and the proton g-factor ($g_p$), since these do not require a "standard meterstick". Here we present a re-analysis of the 18 cm hydroxyl (OH) lines at $z=0.89$, which were recently detected with the MeerKAT telescope, toward the radio source PKS\,1830-211. Utilizing the previous constraint of $\Delta\mu/\mu=(-1.8\pm1.2)\times10^{-7}$, we obtain $\Delta (\alpha g_p^{0.27})/(\alpha g_p^{0.27})\lesssim5.7\times10^{-5}$, $\Delta \alpha/\alpha\lesssim2.3\times10^{-3}$ , and $\Delta g_p/g_p\lesssim7.9\times10^{-3}$. These new constraints are consistent with no evolution over a look-back time of 7.3 Gyr and provide another valuable data point in the putative evolution of the constants.

Figures

Figures reproduced from arXiv: 2505.07200 by the authors.

Figure 1
Figure 1. Gaussian fitting of the OH 18 cm lines. From top to bottom are the OH 1665, 1667, 1612, and 1720 MHz lines. Two Gaussian functions fitted to the OH 1667 MHz line are marked with dotted purple and magenta lines. The corresponding counterparts of these two Gaussian components in other lines in the LTE condition are also marked with dotted purple and magenta lines. The conjugate OH satellite lines (absorption in the 16… view at source ↗
Figure 2
Figure 2. Conjugate OH satellite lines and their summed line. The top and bottom are OH satellite lines with the thermal counterparts subtracted, which have been shifted for clarity, while the middle is the summed spectrum. Both Kolmogorov-Smirnov and Anderson-Darling tests have shown that the summed spectrum is consistent with being drawn from a Gaussian distribution, which strongly suggests that the OH satellite lines are c… view at source ↗

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