Optical clock network tracks tidal variations of the gravity potential

Kilian Stahl; Ingo Nosske; Chetan Vishwakarma; Tim Lücke; Joshua Klose; Erik Benkler; Alexander Kuhl; Shambo Mukherjee; Thomas Legero; Jochen Kronjäger; Uwe Sterr; Christian Lisdat; Sören Dörscher; Chen-Hao Feng; Matthew Y. H. Johnson; Jacques-Olivier Gaudron; Wei Huang; Jacob Tunesi; Xi Zhang; Marco Schioppo; Adam L. Parke; Ian R. Hill; Heiner Denker; Biplab Dutta; Etienne Cantin; Olivier Lopez; Anne Amy-Klein; Christian Chardonnet; Benjamin Pointard; Rodolphe Le Targat; Jérôme Lodewyck; Paul-Eric Pottie; Ichiro Ushijima; Masao Takamoto; Hidetoshi Katori; Yogeshwar B. Kale; Stefano Condio; Irene Goti; Tommaso Petrucciani; Cecilia Clivati; Simone Donadello; Filippo Levi; Davide Calonico; Marco Pizzocaro

AI summary · arXiv: 2610.39635v1 · astro-ph.EP

Optical clock network tracks tidal variations of the gravity potential

Kilian Stahl, Ingo Nosske, Chetan Vishwakarma, Tim Lücke, Joshua Klose, Erik Benkler, Alexander Kuhl, Shambo Mukherjee,

and 36 more authors

Thomas Legero, Jochen Kronjäger, Uwe Sterr, Christian Lisdat, Sören Dörscher, Chen-Hao Feng, Matthew Y. H. Johnson, Jacques-Olivier Gaudron, Wei Huang, Jacob Tunesi, Xi Zhang, Marco Schioppo, Adam L. Parke, Ian R. Hill, Heiner Denker, Biplab Dutta, Etienne Cantin, Olivier Lopez, Anne Amy-Klein, Christian Chardonnet, Benjamin Pointard, Rodolphe Le Targat, Jérôme Lodewyck, Paul-Eric Pottie, Ichiro Ushijima, Masao Takamoto, Hidetoshi Katori, Yogeshwar B. Kale, Stefano Condio, Irene Goti, Tommaso Petrucciani, Cecilia Clivati, Simone Donadello, Filippo Levi, Davide Calonico, Marco Pizzocaro

Original paper Submitted to arXiv on 29 Oct. 2026 License: NONEXCLUSIVE-DISTRIB 1.0 Also in: fr

How to read this summary? Illustrated guide

The essentials

European optical clock comparisons resolved tidal changes in gravity potential differences within one day, extending chronometric levelling from static measurements to dynamic signals.

Question

Can a network of distant optical clocks resolve time-varying gravity potential differences caused by tides, rather than only static differences? Do the measured frequency variations agree with geodetic tidal predictions?

Method

The authors compared strontium and ytterbium optical lattice clocks through phase-stabilized European fibre links during three campaigns in March 2023, March 2025 and June 2025. The main comparisons covered approximately 840 km between INRiM and PTB and 740 km between NPL and PTB, with a transportable clock deployed at INRiM. They compared frequency ratios with a geodetic tide model using three-hour moving averages, Lomb–Scargle periodograms and a linear Kalman filter estimating the signal amplitude relative to predictions.

Findings

Result The clock comparisons resolved predicted tidal variations within one day and agreed with the tide model.
See the passage in the paper
The measured relativistic rate shifts track the tidal variations, resolving the predicted signal within one day of measurement and agreeing with model predictions.
Result Both main baselines showed semidiurnal variations, while substantial diurnal variations appeared only on the NPL–PTB baseline, consistent with their different geographical configurations.
See the passage in the paper
Semidiurnal constituents are dominant in both cases, but the variations between NPL and PTB further contain substantial diurnal constituents.
Result Across the two main week-long comparisons, estimated tidal amplitudes agreed with predictions and differed from zero by more than four standard uncertainties.
See the passage in the paper
Both comparisons took place over the course of one week, including downtimes. The results agree with the model prediction and provide highly significant detections, deviating from zero by more than four times their standard uncertainty.
Result The transportable clock demonstrated that remote sensing of time-varying gravity potential differences can achieve instability similar to stationary clock systems.
See the passage in the paper
In this work, a transportable clock was deployed as a remote sensor of time-varying gravity potential differences. It achieved a similar instability as the stationary systems, thanks to pre-stabilizing its clock laser to a transportable ultrastable optical cavity Herbers et al. (2022).

Limitations

Increased frequency-ratio variability at long averaging times may limit the accuracy of tidal amplitude estimates.
See the passage in the paper
In the present work, the increased variability does not prevent identification of the tidal signal, albeit it may limit the accuracy with which its amplitude can be determined.
Detection performance depends on baseline geometry, measurement timing, clock instability, network availability and measurement duration.
See the passage in the paper
The optical clock network’s ability to detect tidal RRS variations depends on the geographical configuration of the baseline and time of measurement as well as on the instability of the clock comparison, availability of the clock and fibre links and measurement duration.
The study tested clock comparisons against known tidal signals rather than demonstrating monitoring of less well-known geophysical changes.
See the passage in the paper
In the present study, the tides primarily provide a known time-dependent signal, allowing the clock comparisons to be tested against model predictions.

Why it matters

The authors argue that these measurements extend experimental chronometric levelling to dynamic gravity potential differences and establish tidal corrections as necessary for precise remote clock comparisons. With improved clock performance and availability, optical clock networks could complement established geodetic methods by monitoring potential changes associated with deformation and mass redistribution.

Written by AI from the paper. Passages are checked word for word against the text we analysed; the rest may contain errors.

AI-generated keywords: Optical atomic clocks; Chronometric levelling; Time-varying gravity potential; Tidal signals; Optical-fibre networks

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Comprehensive Summary
Layman's Summary
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Original abstract

This paper investigates whether a network of optical atomic clocks can detect changes in Earth’s gravitational potential over time, rather than merely measure static differences between locations. General relativity predicts that gravitational potential affects the rate at which clocks tick. Comparing distant clocks therefore provides a direct measurement of their gravitational-potential difference, a technique known as chronometric levelling. The authors use tidal variations as a predictable test signal. The gravitational influence of the Moon and Sun, together with Earth’s deformation and ocean loading, produces small daily and twice-daily changes in clock rates. The study combines optical lattice clocks with phase-stabilized optical-fibre links connecting European laboratories, using measurements from campaigns conducted in March 2023, March 2025 and June 2025. The two principal comparisons linked PTB in Brunswick, Germany, with INRiM in Torino, Italy, approximately 840 kilometres away, and with NPL in Teddington, United Kingdom, approximately 740 kilometres away. For the Italian comparison, the researchers deployed the transportable strontium clock PTB-Sr4 at INRiM and compared it with PTB-Sr3 in Germany. The British comparison used the stationary clocks NPL-Sr1 and PTB-Sr3. Additional comparisons involving strontium and ytterbium clocks provided supporting measurements. A geodetic model predicted the time-dependent relativistic rate shifts, accounting for celestial tide-generating potentials, solid Earth tides, ocean tidal loading and smaller tidal effects. Although the predicted fractional rate variations at individual stations were around 4 × 10⁻¹⁷, much of the signal was common to both ends of each comparison. The differential variations reached only about 5 × 10⁻¹⁸ peak to peak, requiring exceptional stability over several hours to resolve. The principal Italian and British comparisons achieved fractional frequency instabilities of approximately 4.7 × 10⁻¹⁶ and 3.8 × 10⁻¹⁶, respectively, each divided by the square root of the averaging time in seconds. The researchers assessed agreement with the model using three complementary methods: three-hour moving averages, Lomb–Scargle spectral analysis and a Kalman filter that progressively estimated the tidal signal’s amplitude relative to the prediction. Both principal comparisons showed significant twice-daily oscillations. The British–German comparison also exhibited a substantial daily component, whereas the Italian–German comparison did not, consistent with their different baseline geometries. Subtracting the predicted tidal signal strongly suppressed these spectral features, supporting agreement in both amplitude and phase. The Kalman filter yielded relative amplitudes of 1.42 ± 0.35 for INRiM–PTB and 1.12 ± 0.24 for NPL–PTB, with a value of one indicating exact agreement with the model. Both week-long campaigns, including measurement interruptions, detected the signal at more than four standard uncertainties above zero. Daily estimates with sufficient measurement coverage were consistent with predictions, demonstrating that the variations could be resolved within a day, although individual daily detections were less statistically significant. Across all reported comparisons, the weighted mean amplitude was 1.00 ± 0.12. The authors conclude that optical-clock networks can extend chronometric levelling from static measurements to dynamic gravitational-potential sensing, including with a transportable clock. Sensitivity nevertheless depends on geographical configuration, clock stability, measurement uptime and campaign duration. Unexplained excess variability at long averaging times may limit amplitude accuracy, although fibre-link noise was not the limiting factor in this study. The experiment measured known tidal signals rather than detecting unknown geophysical changes. Improved clocks and greater network availability could eventually enable monitoring of deformation and mass redistribution. Meanwhile, tidal corrections are already necessary for remote clock comparisons targeting fractional uncertainties near 10⁻¹⁸ or below.

Optical Clocks Track Earth’s Changing Gravitational Potential

The Moon and Sun do more than drive ocean tides. Their gravitational influence also deforms Earth and subtly changes how quickly atomic clocks tick. A new study shows that a network of optical clocks can follow these tiny variations over time, opening a path toward measuring a changing planet through the passage of time itself.

In “Optical clock network tracks tidal variations of the gravity potential,” Kilian Stahl, Ingo Nosske, Chetan Vishwakarma, Tim Lücke, Joshua Klose, Erik Benkler et al. demonstrate that clocks connected across Europe can detect predictable tidal changes in gravitational potential. The achievement extends a technique called chronometric levelling beyond static comparisons between locations.

When Gravity Changes, So Does Time

General relativity predicts that a clock’s ticking rate depends on its gravitational potential. Comparing two sufficiently precise clocks therefore reveals the difference in gravitational potential between their locations. This offers a way to connect timekeeping with geodesy, the science of measuring Earth’s shape and gravitational field.

Measuring a fixed difference is one challenge. Tracking small changes over hours is another. Clock noise must remain low enough that a weak, time-varying signal can emerge. Tides provide an ideal test: their timing and behaviour can be predicted, allowing researchers to compare clock measurements against an independently calculated model.

The relevant effects extend beyond the direct gravitational pull of the Moon and Sun. Earth’s solid surface deforms, and moving ocean water loads the crust. Together, these processes produce daily and twice-daily changes in the rates of clocks at different locations.

A Precision Network Across Europe

The study used optical lattice clocks connected through phase-stabilized optical-fibre links, drawing on measurement campaigns in March 2023, March 2025 and June 2025. Two comparisons formed the core of the investigation:

PTB in Brunswick, Germany, and INRiM in Torino, Italy, separated by approximately 840 kilometres.
PTB and NPL in Teddington, United Kingdom, separated by approximately 740 kilometres.

For the Italian comparison, the researchers deployed PTB’s transportable strontium clock, PTB-Sr4, at INRiM and compared it with PTB-Sr3 in Germany. The British comparison used the stationary strontium clocks NPL-Sr1 and PTB-Sr3. Additional measurements involving strontium and ytterbium clocks supported the analysis.

A Tiny Signal Hidden in Shared Motion

The geodetic model predicted fractional clock-rate variations of around 4 × 10⁻¹⁷ at individual stations. However, much of that variation was shared between the two ends of each comparison. Because the experiment measured their difference, the remaining signal reached only about 5 × 10⁻¹⁸ peak to peak.

Resolving such a small difference required exceptional stability over several hours. The Italian and British comparisons achieved fractional frequency instabilities of approximately 4.7 × 10⁻¹⁶ and 3.8 × 10⁻¹⁶, respectively, divided by the square root of the averaging time in seconds. Longer averaging helped bring the tidal signal into view.

Three Ways to Check the Tidal Signature

The researchers examined the measurements using three complementary approaches: three-hour moving averages, Lomb–Scargle spectral analysis and a Kalman filter. These methods helped reveal changes over time, identify periodic signals and progressively estimate the measured tidal amplitude relative to the model.

Both principal comparisons showed significant twice-daily oscillations. The British–German comparison also displayed a substantial daily component, while the Italian–German comparison did not. This difference matched expectations from the geographical arrangement of the stations: the network’s geometry determines how much of the tidal variation survives when one clock’s rate is compared with another’s.

Subtracting the predicted tidal signal strongly suppressed those spectral features. This supported agreement not just in the size of the oscillations, but also in their timing.

How Closely Did Measurement Match Prediction?

The Kalman filter estimated relative amplitudes of 1.42 ± 0.35 for INRiM–PTB and 1.12 ± 0.24 for NPL–PTB. A value of one represents exact agreement with the predicted amplitude. Both week-long campaigns detected the signal at more than four standard uncertainties above zero, despite measurement interruptions.

Across all reported comparisons, the weighted mean amplitude was 1.00 ± 0.12. Daily estimates with sufficient coverage were also consistent with predictions, showing that the variations could be resolved within a day, although individual daily detections were less statistically significant.

From a Tidal Test to Future Earth Monitoring

The experiment detected known tidal signals, not previously unknown geophysical changes. That distinction matters: this is a demonstration of dynamic gravitational-potential sensing, rather than an operational system for discovering deformation or mass redistribution.

Important limitations remain. Sensitivity depends on station geography, clock stability, measurement uptime and campaign duration. Unexplained excess variability at long averaging times may constrain amplitude accuracy, although fibre-link noise was not the limiting factor here.

Even so, the results show that optical-clock networks—including transportable clocks—can extend chronometric levelling into the time domain. Better clocks and more continuously available networks could eventually help monitor Earth’s changing mass distribution and deformation. For today’s precision timekeeping, the message is already practical: remote clock comparisons targeting fractional uncertainties near 10⁻¹⁸ or below must account for tides.

Created on 02 Nov. 2026

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Optical clock network tracks tidal variations of the gravity potential

The essentials

Question

Method

Findings

Limitations

Why it matters

Read further

Definitions

Optical Clocks Track Earth’s Changing Gravitational Potential

When Gravity Changes, So Does Time

A Precision Network Across Europe

A Tiny Signal Hidden in Shared Motion

Three Ways to Check the Tidal Signature

How Closely Did Measurement Match Prediction?

From a Tidal Test to Future Earth Monitoring

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