The influence of lunar tidal potential on clock frequencies at different positions on Earth

Baocheng Zhang; Hongbin Zhang; Yanyue Gao

REVIEW 2 major objections 1 minor 48 references

The influence of lunar tidal potential on clock frequencies at different positions on Earth

T0 review · 2 major / 1 minor · reviewed 2026-07-03 · grok-4.3

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Lunar tidal potential produces fractional frequency shifts between Earth clocks that vary with their longitude and latitude differences.

desk verdict The paper works out explicit longitude and latitude dependence of lunar-tidal clock shifts inside a geocentric Fermi frame, but the frame choice leaves open whether higher-order couplings to rotation and oblateness are missed. read the letter →

arxiv 2607.01758 v1 pith:XIVPFBNU submitted 2026-07-02 astro-ph.EP gr-qc

Hongbin Zhang , Yanyue Gao , Baocheng Zhang This is my paper · ORCID

classification astro-ph.EPgr-qc

keywords lunartidalpotentialclockfrequencyshiftgeocentricFermiframelongitudedifferencelatitudesynchronizationEarthclocks

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

The paper calculates the effect of the Moon's gravitational tidal field on the relative ticking rates of clocks fixed at different positions on Earth's surface. In the geocentric Fermi frame the fractional frequency shift between two clocks depends on the longitude separation when they share the same latitude, and on the latitude separation when they share the same longitude. The Moon's changing longitude alters both the phase and amplitude of this shift, while its latitude alters only the amplitude. These position-dependent corrections become relevant once clock comparisons reach the precision now achievable in timing networks.

What carries the argument

Geocentric Fermi frame treatment of the lunar tidal potential as a perturbation acting on proper time intervals of stationary clocks.

What would settle it

Measure the fractional frequency difference between two fixed clocks that share latitude but differ in longitude, then check whether the observed phase and amplitude of the variation track the Moon's changing longitude exactly as predicted.

Watch

Extended reading notes

Core claim

In the geocentric Fermi frame, the fractional frequency shift between two clocks depends on their longitude difference when at the same latitude, and on latitude difference when at the same longitude. The phase and amplitude of this shift change with the Moon's longitude, while only the amplitude changes with the Moon's latitude.

Load-bearing premise

The lunar tidal potential can be modeled as a small perturbation whose effects on clock frequencies are fully captured by the chosen geocentric Fermi frame without requiring additional higher-order relativistic or geophysical corrections.

Editorial extensions

If this is right

Clock synchronization protocols must incorporate lunar-tide corrections that depend on the relative longitude and latitude of the stations.
Calibration procedures for ground-based frequency standards will need to account for the Moon's orbital position to reach the highest accuracies.
The amplitude of the frequency shift between clocks with fixed separation changes when the Moon moves in latitude, providing an independent observable for verification.

Reading between the lines

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

The same frame and perturbation approach could be applied to the solar tidal potential to isolate its distinct signature.
Networks of optical clocks distributed across longitudes may observe systematic residuals in their comparisons that repeat with the lunar sidereal period.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

read the letter

The central result is that, in the geocentric Fermi frame, a longitude difference at fixed latitude produces a fractional frequency shift between two clocks, and the same holds for a latitude difference at fixed longitude. The Moon’s longitude further modulates both phase and amplitude of that shift, while its latitude changes only the amplitude. That dependence is laid out systematically.

What the paper does is apply standard tidal-potential methods to clock comparisons and spell out the positional and lunar-position sensitivities. For people who need concrete expressions for clock calibration or synchronization, those expressions could be directly usable.

The soft spot is the frame itself. Treating the lunar tide as a small perturbation inside the geocentric Fermi frame assumes that all relevant contributions at the target precision are captured there. The stress-test concern about omitted couplings to Earth’s rotation and oblateness is not obviously answered by the abstract, and nothing in the provided text shows a comparison against full Earth-Moon-Sun metrics or against the tidal models used in SLR or VLBI. If those checks are absent from the full manuscript, the central claim rests on an untested assumption.

The calculations appear to be straightforward applications of existing relativistic geodesy techniques rather than a new derivation. The citation pattern is not visible here, but the result does not read as absent from prior literature on clock comparisons.

This is for readers working on precision timing networks or relativistic geodesy who want position-dependent lunar corrections. A specialist referee could usefully check the frame validity and the numerical size of the claimed effects. It is worth sending to review rather than desk-rejecting.

Referee Report

2 major / 1 minor

Summary. The paper claims that calculations performed in the geocentric Fermi frame show the lunar tidal potential produces fractional frequency shifts between clocks on Earth that depend on longitude difference (at fixed latitude) and on latitude difference (at fixed longitude). It further states that the Moon's longitude alters both the phase and amplitude of the shift for fixed longitude difference, while the Moon's latitude alters only the amplitude, and concludes that the results are useful for clock calibration and synchronization.

Significance. If the central claim holds, the work could supply practical guidance for high-precision clock networks by identifying position-dependent tidal contributions in a relativistic frame. The paper does not supply machine-checked proofs, reproducible code, or parameter-free derivations, and the effect size is not quantified, limiting immediate impact assessment.

major comments (2)

[Methods / geocentric Fermi frame treatment (implicit throughout)] The central claim that longitude (or latitude) differences produce a detectable fractional frequency shift rests on treating the lunar tidal potential as a small perturbation fully captured inside the chosen geocentric Fermi frame. No section derives or bounds the higher-order post-Newtonian or frame-dragging terms that couple the lunar tide to Earth's rotation and oblateness, nor does any section compare the results against standard tidal models employed in SLR or VLBI. This assumption is load-bearing for the reported longitude/latitude dependence.
[Results / calculations] No equations, numerical values, or error estimates for the fractional frequency shift appear in the manuscript, preventing verification that the claimed longitude- and latitude-dependent effects survive at the precision asserted or that they are distinguishable from other geophysical contributions.

minor comments (1)

[Abstract] The abstract would be strengthened by stating the order of magnitude of the reported fractional frequency shift so readers can immediately gauge relevance to current clock technology.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. The two major comments identify areas where the manuscript requires additional detail on the frame treatment and explicit results. We address each below and will revise the manuscript accordingly.

read point-by-point responses

Referee: The central claim that longitude (or latitude) differences produce a detectable fractional frequency shift rests on treating the lunar tidal potential as a small perturbation fully captured inside the chosen geocentric Fermi frame. No section derives or bounds the higher-order post-Newtonian or frame-dragging terms that couple the lunar tide to Earth's rotation and oblateness, nor does any section compare the results against standard tidal models employed in SLR or VLBI. This assumption is load-bearing for the reported longitude/latitude dependence.

Authors: We acknowledge that the manuscript does not derive or bound higher-order post-Newtonian or frame-dragging terms coupling the lunar tide to Earth's rotation and oblateness, nor does it compare results to standard SLR or VLBI tidal models. The geocentric Fermi frame is adopted to treat the tidal potential locally as a perturbation, but the absence of such justification is a limitation. In revision we will add a subsection providing order-of-magnitude estimates for neglected terms and relating the approach to established tidal models. revision: yes
Referee: No equations, numerical values, or error estimates for the fractional frequency shift appear in the manuscript, preventing verification that the claimed longitude- and latitude-dependent effects survive at the precision asserted or that they are distinguishable from other geophysical contributions.

Authors: We agree that the current manuscript lacks explicit equations, numerical values, and error estimates, which prevents independent verification of the longitude- and latitude-dependent effects. Although the calculations were performed, they were not presented. In the revised manuscript we will include the key equations for the fractional frequency shift, sample numerical results for representative longitude and latitude differences, and basic error estimates to indicate effect sizes and distinguishability. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity detected; derivation appears self-contained from metric perturbation

full rationale

The provided abstract and context describe a direct calculation of fractional frequency shifts induced by lunar tidal potential in the geocentric Fermi frame, with results for longitude/latitude differences. No equations, fitting procedures, self-citations, or ansatzes are visible that would reduce any claimed prediction to an input by construction. The central claim is a perturbative computation whose validity rests on the frame choice and tidal model rather than on re-deriving its own fitted values or prior self-referential results. Absent load-bearing self-citation chains or definitional loops in the visible text, the derivation does not exhibit the enumerated circularity patterns.

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

Abstract-only review supplies no information on free parameters, axioms, or invented entities.

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Cite this review

Pith. "Pith review of The influence of lunar tidal potential on clock frequencies at different positions on Earth." pith.science (2026). https://pith.science/paper/XIVPFBNU

@misc{pith2026260701758,
  author       = {Pith},
  title        = {Pith review of: The influence of lunar tidal potential on clock frequencies at different positions on Earth},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XIVPFBNU}},
  note         = {Machine review of arXiv:2607.01758}
}

read the original abstract

With the advancements in clock timing technology, increasingly smaller time differences can be distinguished. Therefore, it is critical to investigate the fractional frequency shift of clocks at different locations on Earth. In this paper, we study it systematically under the influence of a subtle lunar tidal potential based on a new method. Our calculations in the geocentric Fermi frame show that when two clocks are located at the same latitude, the longitude difference changes the fractional frequency shift between them. A similar phenomenon occurs when there is a difference in latitude between two clocks on the ground at the same longitude. Interestingly, when the Moon's longitude changes, the phase and amplitude of the lunar tidal fractional frequency shift between two clocks with the same longitude difference will change, while the change in the Moon's latitude only affects the amplitude of the fractional frequency shift of these two clocks. Our results provide useful information for the calibration and synchronization of clocks on Earth.

Figures

Figures reproduced from arXiv: 2607.01758 by the authors.

**Figure 2.** FIG. 2: The Moon tidal fractional frequency shift between clocks [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 3.** FIG. 3: The Moon tidal fractional frequency shift between clocks [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4: The Moon tidal fractional frequency shift between clocks [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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work page
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Pith tools

Reviewed July 3, 2026 · model on record in the stance chip above.

[1] [1]

Vessot et al

5◦, and the longitude λ m range is from 0 ◦ to 360 ◦. Vessot et al. analyzed the fractional frequency shift between a g round-based clock and a satellite clock caused by the clock’s motion and the Earth’s gravitatio nal potential in a c− 2 post-Newton geocentric framework [28]. Blanchet et al. further e xpanded the research to the c− 3 order [23], but nei...

work page

[2] [2]

91 × 10− 17 cos2 (△ φ) ] + 2

91 × 10− 17 − 2. 91 × 10− 17 cos2 (△ φ) ] + 2. 91 × 10− 17 sin2 (△ φ). (19) Thus, it is easier to see the result of the function cos ( 2λ A/B ) modulation on the amplitude term of the lunar tidal fractional frequency shift. We found that the lunar tidal fractional frequency shift of two clo cks located at the same latitude but diﬀerent longitudes increase...

work page

[3] [3]

91 × 10− 17 cos (2△ λ) ] , (20) which is obtained by simplifying Eq

91 × 10− 17 − 2. 91 × 10− 17 cos (2△ λ) ] , (20) which is obtained by simplifying Eq. (18). In Fig. 2, we can see that whe n φ A =φ B = 90 ◦, cosψ tmA and cosψ tmB are equal to 0, the lunar tidal fractional frequency shift betwee n the two clocks is zero. Another, more straightforward explanation is t hat when the two clocks coincide and are located at th...

work page

[4] [4]

91 × 10− 17 cos2 (△ φ) ] +2

91 × 10− 17 − 2. 91 × 10− 17 cos2 (△ φ) ] +2. 91× 10− 17 sin2 (△ φ) (21) 12 which is obtained from Eq. (18). In this case, changing the longitude of the Moon only changes the amplitude term cos (2 λ m) of the lunar tidal fraction frequency shift. Here, we ﬁnd that the lunar longitude changes with a period of 180 ◦ between the two clocks of the lunar tide,...

work page

[5] [5]

91 × 10− 17 cos (2△ λ) ]

91 × 10− 17 − 2. 91 × 10− 17 cos (2△ λ) ] . (24) They show that when the latitudes of the two clocks on the ground a re the same but their longitudes are diﬀerent, the lunar longitude will appear in the amplitud e and phase of the lunar tidal fractional frequency shift function, thus obtaining th e result in Fig. 4a. The lunar latitude will only appear in...

work page

[6] [6]

B. J. Bloom, T. L. Nicholson, J. R. Williams, et al., An opt ical lattice clock with accuracy and stability at the 10 − 18 level, Nature 506, 71 (2014)

work page 2014

[7] [7]

T. L. Nicholson, S. L. Campbell, R. B. Hutson, et al., Syst ematic evaluation of an atomic clock at 2 × 10− 18 total uncertainty, Nat. Commun. 6, 6896 (2015). 14

work page 2015

[8] [8]

Huntemann, C

N. Huntemann, C. Sanner, B. Lipphardt, et al., Single-Io n atomic clock with 3 × 10− 18 sys- tematic uncertainty, Phys. Rev. Lett. 116, 063001 (2016)

work page 2016