Test of Special Relativity Using a Fiber Network of Optical Clocks
Open accessAbstract
Phase compensated optical fiber links enable high accuracy atomic clocks separated by thousands of kilometers to be compared with unprecedented statistical resolution. By searching for a daily variation of the frequency difference between four strontium optical lattice clocks in different locations throughout Europe connected by such links, we improve upon previous tests of time dilation predicted by special relativity. We obtain a constraint on the Robertson-Mansouri-Sexl parameter |α|≲1.1×10^{-8}, quantifying a violation of time dilation, thus improving by a factor of around 2 the best known constraint obtained with Ives-Stilwell type experiments, and by 2 orders of magnitude the best constraint obtained by comparing atomic clocks. This work is the first of a new generation of tests of fundamental physics using optical clocks and fiber links. As clocks improve, and as fiber links are routinely operated, we expect that the tests initiated in this Letter will improve by orders of magnitude in the near future.
AI snapshot
Written from the paper’s full text.
TL;DR
The paper searches for a daily variation in the frequency difference between four strontium optical lattice clocks in France, Germany, and the United Kingdom connected by phase-compensated fiber links, as a test of time dilation in special relativity. It constrains the Robertson-Mansouri-Sexl Lorentz-invariance-violating parameter to \(|\alpha| \lesssim 1.1 \times 10^{-8}\), improving the best Ives-Stilwell constraint by about a factor of 2 and the best atomic-clock constraint by 2 orders of magnitude.
Key findings
- The combined NPL-SYRTE fit gives \(\alpha_C = (-2.83 \pm 6.19) \times 10^{-8}\); the PTB-SYRTE fit gives \(\alpha_D = (-0.38 \pm 1.06) \times 10^{-8}\).
- The final bound is \(|\alpha| \lesssim 1.1 \times 10^{-8}\), improving the best previous Ives-Stilwell-type constraint by around a factor of 2 and the best atomic-clock comparison constraint by 2 orders of magnitude.
- In the PTB-SYRTE comparison, a significant temperature effect on the frequency comparison was found at the order of \(10^{-16}\,\mathrm{K}^{-1}\), with a lag of around 4.8 h; the bias on \(\alpha\) is \(-0.93 \times 10^{-8}\) if tides are not taken into account.
- The NPL-SYRTE comparisons did not show significant systematic effects above the noise level, and a simulated temperature model using PTB-SYRTE parameters produced no signal above noise for NPL-SYRTE.
Methods
- Design: compare four Sr optical lattice clocks—two at LNE-SYRTE in France, one at PTB in Germany, and one at NPL in the United Kingdom—connected by phase-compensated optical fiber links, and search for a sidereal-day variation in the relative frequency difference predicted by the Robertson-Mansouri-Sexl framework.
- Data: NPL-SYRTE comparison from June 10–15, 2016, with about 60 h of data between SYRTE’s Sr2 and SrB clocks and NPL’s Sr clock; PTB-SYRTE comparison from June 4–24, 2015, with about 150 h of data between SYRTE’s Sr2 clock and PTB’s stationary Sr clock.
- Analysis: fit models including the Lorentz-invariance-violating term \(2\alpha c^{-2}\vec{w}\cdot[\vec{v}_{\mathrm{SYRTE}}(t)-\vec{v}_{\mathrm{other}}(t)]\), using an affine invariant Markov Chain Monte Carlo ensemble sampler with \(10^5\) points and a nondiagonal covariance matrix; for PTB-SYRTE, a temperature model for the SYRTE clock room was included. The preferred frame is taken as the CMB rest frame, with \(w \simeq 340\,\mathrm{km\,s^{-1}}\) in June 2015 and 2016.
Limitations
- The paper states that the RMS framework is purely kinematical and the results cannot be simply mapped to dynamical frameworks such as the standard model extension or dark matter models.
- The paper states that the temperature effect on the PTB-SYRTE comparison is not yet fully understood, and that the lag \(\delta t_{\mathrm{SYRTE}}\) is not well constrained and its distribution is non-Gaussian.
- The paper states that combining data sets A, B, and D gives no improvement on the uncertainty because the absolute bias in combination C is larger than the uncertainty from data set D; the text also makes evident that the test relies on limited-duration comparisons and technical noise sources.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
0 of 23 cited sources checked · 0 supported · 0 flagged
- Findingown data
The power spectral density distribution of the raw data shows a significant peak at a frequency of 1 day^-1, which is around the frequency of the Lorentz-invariance-violating signal.
“Indeed, the power spectral density distribution of the raw data shows a significant peak at a frequency of 1 day -1 , which is around the frequency of the LI violating signal.”
Quote in the paperSubstantial claim - Findingown data
The bias of the parameter |alpha| is below the parameter uncertainty: alpha_D = (-0.38 +/- 1.06) x 10^-8.
“The bias of the parameter jαj is below the parameter uncertainty: α D ¼ ð-0.38 Æ 1.06Þ × 10 -8 :ð11Þ”
Quote in the paperSubstantial claim- The authors state this as an assumption: The Robertson-Mansouri-Sexl framework assumes the existence of a preferred frame Sigma where light propagates rectilinearly and isotropically in free space with constant speed c.
- The authors state this as an assumption: The preferred frame is taken as the rest frame of the cosmological microwave background (CMB).
- Findingown data
The constraint improves by 2 orders of magnitude the best constraint obtained by comparing atomic clocks.
“and by 2 orders of magnitude the best constraint obtained by comparing atomic clocks.”
Quote in the paperSubstantial claim - Findingown data
By using clock comparisons between four optical clocks at NPL, PTB, and SYRTE, linked by an optical fiber network, the work puts a more stringent bound on the Lorentz-invariance-violating parameter alpha of the RMS framework.
“In conclusion, by using clock comparisons between four optical clocks at NPL (United Kingdom), PTB (Germany), and SYRTE (France), linked by a leading-edge optical fiber network, we are able to put a more stringent bound on the LI violating parameter α of the RMS framework.”
Quote in the paperSubstantial claim- The authors state this as an assumption: The Robertson-Mansouri-Sexl framework assumes the existence of a preferred frame Sigma where light propagates rectilinearly and isotropically in free space with constant speed c.
- The authors state this as an assumption: The preferred frame is taken as the rest frame of the cosmological microwave background (CMB).
- Findingown data
The constraint on the Robertson-Mansouri-Sexl parameter is |alpha| <~ 1.1 x 10^-8.
“We obtain a constraint on the Robertson-Mansouri-Sexl parameter jαj ≲ 1.1 × 10 -8 , quantifying a violation of time dilation”
Quote in the paperSubstantial claim- The authors state this as an assumption: The Robertson-Mansouri-Sexl framework assumes the existence of a preferred frame Sigma where light propagates rectilinearly and isotropically in free space with constant speed c.
- The authors state this as an assumption: The preferred frame is taken as the rest frame of the cosmological microwave background (CMB).
- Findingown data
The constraint improves by a factor of around 2 the best known constraint obtained with Ives-Stillwell type experiments.
“thus improving by a factor of around 2 the best known constraint obtained with Ives-Stilwell type experiments”
Quote in the paperSubstantial claim - Findingown data
A simulation of the temperature model (9) for the NPL-SYRTE comparisons, using the parameters determined in the PTB-SYRTE comparison, does not produce any signal above the noise level.
“Consistently, a simulation of the temperature model ( 9) for the NPL-SYRTE comparisons, using the parameters determined in the PTB-SYRTE comparison, does not produce any signal above the noise level.”
Quote in the paperSubstantial claim - Findingown data
The best result is found when combining the two sets of data: alpha_C = (-2.83 +/- 6.19) x 10^-8.
“The best result is found when combining the two sets of data: α C ¼ ð-2.83 Æ 6.19Þ × 10 -8 :ð8Þ”
Quote in the paperSubstantial claim- The authors state this as an assumption: The Robertson-Mansouri-Sexl framework assumes the existence of a preferred frame Sigma where light propagates rectilinearly and isotropically in free space with constant speed c.
- The authors state this as an assumption: The preferred frame is taken as the rest frame of the cosmological microwave background (CMB).
- Findingown data
An analysis of the PTB-SYRTE comparison data with a model similar to Eq. (7) results in a significant bias for the parameter alpha, 5 times larger than the 1-sigma uncertainty on alpha.
“An analysis of the PTB-SYRTE comparison data with a model similar to Eq. ( 7) (replacing the NPL clock velocity with the PTB clock velocity, and i ¼ fSr2g) results in a significant bias for the parameter α, 5 times larger than the 1σ uncertainty on α.”
Quote in the paperSubstantial claim- The authors state this as an assumption: The Robertson-Mansouri-Sexl framework assumes the existence of a preferred frame Sigma where light propagates rectilinearly and isotropically in free space with constant speed c.
- The authors state this as an assumption: The preferred frame is taken as the rest frame of the cosmological microwave background (CMB).
- Findingreasoning
A combination of the three data sets A, B, and D has been evaluated but gives no improvement on the uncertainty of the determination of the Lorentz-invariance-violating parameter.
“A combination of the three data sets A, B, and D has been evaluated but gives no improvement on the uncertainty of the determination of the LI violating parameter.”
Quote in the paperNot a substantial claim - Findingown data
A detailed analysis of the NPL-SYRTE comparisons did not show any significant systematic effects above the noise level.
“A detailed analysis of the NPL-SYRTE comparisons did not show any significant systematic effects above the noise level.”
Quote in the paperSubstantial claim - Findingown data
This work improves upon the best previous constraint on the Lorentz-invariance-violating parameter alpha by a factor of around 2.
“In this Letter, we improve upon this best previous constraint on the LI violating parameter α by a factor of around 2.”
Quote in the paperSubstantial claim - Premisereasoning
It is possible to bound the Lorentz-invariance-violating parameter alpha by looking for daily variations in the relative frequency difference y between remote clocks located at different longitudes and/or different latitudes.
“It is therefore possible to bound the LI violating parameter α by looking for daily variations in the relative frequency difference y between remote clocks, located at different longitudes (i.e., different orientation of ⃗v) and/or different latitudes (i.e., different norms of ⃗v).”
Quote in the paperSubstantial claim- The authors state this as an assumption: The Robertson-Mansouri-Sexl framework assumes the existence of a preferred frame Sigma where light propagates rectilinearly and isotropically in free space with constant speed c.
- Premisecitation
A strong violation of Lorentz invariance at the Planck scale is likely to yield a small amount of violation at low energy, which could be measured with precise experiments.
“Indeed, a strong violation of LI at the Planck scale is likely to yield a small amount of violation at low energy, which could be measured with precise experiments [1].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [1] source
Not checked in the free run.
- Interpretationreasoning
The work shows significant potential for tests of fundamental physics with networks of optical clocks connected by optical fiber links.
“This shows the significant potential for tests of fundamental physics with networks of optical clocks connected by optical fiber links.”
Quote in the paperNot a substantial claim - Premisecitation
Phase-compensated optical fiber links enable high-accuracy atomic clocks separated by thousands of kilometers to be compared with unprecedented statistical resolution.
“Phase compensated optical fiber links enable high accuracy atomic clocks separated by thousands of kilometers to be compared with unprecedented statistical resolution.”
- Also stated in: § Abstract · plain
“The connection between these clocks, achieved with phase-compensated optical fibers, allows for an unprecedented level of statistical resolution for the comparison of remote atomic clocks [9], making such a test possible for the first time.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [9] source
Not checked in the free run.
- Also stated in: § Abstract · plain
- Premisecitation
The experiment in Ref. [17] uses 7Li+ ions confined at a velocity of 33.8% of the speed of light.
“The experiment described in Ref. [17] uses 7 Li þ ions confined at a velocity of 33.8% of the speed of light.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [17] source
Not checked in the free run.
- Premisecitation
Ives-Stillwell type experiments using heavy-ion storage rings now give the best constraint on alpha.
“With the advent of heavy-ion storage rings, Ives-Stillwell type experiments now give the best constraint on α [16,17].”
Quote in the paperNot a substantial claim0 of 2 sources checked - Premisenone given
The first term of the Lorentz-invariance violation in Eq. (6) varies with a period of one sidereal day as the Earth rotates around its axis.
“The first term of the LI violation in Eq. ( 6) varies with a period of one sidereal day as the Earth rotates around its axis.”
Quote in the paperSubstantial claim- The authors state this as an assumption: The Robertson-Mansouri-Sexl framework assumes the existence of a preferred frame Sigma where light propagates rectilinearly and isotropically in free space with constant speed c.
- Interpretationown data
The lack of improvement from combining A, B, and D is due to the absolute value of the bias on alpha obtained in combination C (2.83 x 10^-8) being larger than the uncertainty obtained with data set D (1.06 x 10^-8).
“This is due to the fact that the absolute value of the bias on α obtained in combination C (2.83 × 10 -8 ) is larger that the uncertainty obtained with data set D (1.06 × 10 -8 ).”
Quote in the paperSubstantial claim - Interpretationown data
The absence of a temperature-model signal in the NPL-SYRTE comparisons justifies not using the temperature model (9) for those comparisons.
“This justifies the fact that the temperature model ( 9) was not used for the NPL-SYRTE comparisons.”
Quote in the paperSubstantial claim
- May combine two claims. 18
- Classified as probably not a substantial claim. 16
- The quote only partly states this claim. 1
May combine two claims.
Findingnone givenThe lag delta_t_SYRTE is not well constrained and its distribution is non-Gaussian; however, this does not affect the Gaussianity of the other parameters.
“The lag δt SYRTE is not well constrained and its distribution is non-Gaussian.However, this does not affect the Gaussianity of the other parameters.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Findingown dataThe correlations between the parameters are of the order or below 0.2.
“The correlations between the parameters are of the order or below 0.2.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataThe frequency instability of the fractional frequency difference between SYRTE and NPL is solely limited by the performances of the clocks, as the fiber link between SYRTE and NPL shows a fractional frequency instability of 1 x 10^-18 at 1000 s.
“This frequency instability is solely limited by the performances of the clocks, as the fiber link between SYRTE and NPL shows a fractional frequency instability of 1 × 10 -18 at 1000 s.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataA significant variation was found at 1 day^-1 frequency in the local SYRTE comparison, while the comparison at PTB did not show any significant variation at this frequency.
“A significant variation was found at 1 day -1 frequency in the local SYRTE comparison, while the comparison at PTB did not show any significant variation at this frequency.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe correlations between the parameter alpha and the parameters ybar_Sr2_PTB-SYRTE, delta_t_SYRTE, and alpha_SYRTE_T are, respectively, -0.48, 0.44, and 0.30; these correlations slightly degrade the uncertainty on the determination of alpha.
“The correlations between the parameter α and the parameters ȳSr2 PTB-SYRTE , δt SYRTE , and α SYRTE T are, respectively, -0.48, 0.44, and 0.30.These correlations slightly degrade the uncertainty on the determination of α.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataNone of the other temperature series (SYRTE exterior, PTB exterior, PTB clock room, PTB clock laser room, PTB comb room) are able to explain the residual signal, leading to biases in alpha ranging from 2 sigma up to 5.5 sigma.
“None of them are able to explain the residual signal, leading for the series (i-v) to biases in the parameter α ranging from 2σ up to 5.5σ”
Quote in the paperSubstantial claimMay combine two claims.
FindingcitationDuring the considered dates of clock comparisons, peak-to-peak fractional frequency variations up to 1.3 x 10^-17 between PTB and SYRTE, and up to 5 x 10^-18 between NPL and SYRTE, are due to variations of the gravity potential induced by tides.
“During the considered dates of clock comparisons, peak-topeak fractional frequency variations up to 1.3 × 10 -17 between PTB and SYRTE, and up to 5 × 10 -18 between NPL and SYRTE are due to variations of the gravity potential induced by tides.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [28] source
Not checked in the free run.
The quote only partly states this claim.
Findingown dataThe Allan deviation of the fractional frequency difference between SYRTE's clocks Sr2 and SrB and NPL's Sr clock is flat up to around 10 s averaging time.
“As can be seen in Fig. 1, the Allan deviation is flat up to around 10 s averaging time.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Findingown dataThe bias found for the parameter alpha is -0.93 x 10^-8 if tides are not taken into account.
“It is interesting to note that the bias found for the parameter α is -0.93 × 10 -8 if tides are not taken into account.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Findingnone givenIn the short term the laser probing the narrow transition is not yet locked to the atoms; therefore, the flicker floor of the free running laser is visible.
“Indeed, in the short term the laser probing the narrow transition is not yet locked to the atoms; therefore, the flicker floor of the free running laser is visible.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataThe detailed analysis of the PTB-SYRTE data shows a significant effect of temperature on the frequency comparison of the order of 10^-16 K^-1, with a lag of around 4.8 h.
“It shows a significant effect of the temperature on the frequency comparison of the order of 10 -16 K -1 , with a lag of around 4.8 h.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
InterpretationcitationOne major limitation of the RMS framework is that it is purely kinematical, and the results cannot be simply mapped to dynamical frameworks.
“As noted in Ref. [14], one major limitation of the RMS framework is that it is purely kinematical, and our results cannot be simply mapped to dynamical frameworks.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [14] source
Not checked in the free run.
- The authors state this as an assumption: The Robertson-Mansouri-Sexl framework assumes the existence of a preferred frame Sigma where light propagates rectilinearly and isotropically in free space with constant speed c.
May combine two claims.
InterpretationcitationThe second term of Eq. (6) is constant and, considering an upper bound of 2 x 10^-8 on alpha, is lower than 4 x 10^-20, which is significantly below the accuracy of the clocks; therefore it is not taken into account in the model.
“The second term of Eq. ( 6) is constant, and, considering an upper bound of 2 × 10 -8 on the parameter α [17], is lower than 4 × 10 -20 , which is significantly below the accuracy of the clocks.Therefore we do not take it into account in our model.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [17] source
Not checked in the free run.
- The authors state this as an assumption: The Robertson-Mansouri-Sexl framework assumes the existence of a preferred frame Sigma where light propagates rectilinearly and isotropically in free space with constant speed c.
May combine two claims.
Interpretationown dataQ0 for the PTB-SYRTE link is more than twice the value for the NPL-SYRTE link, such that it is more sensitive to a violation of Lorentz invariance.
“Note that Q 0 for the PTB-SYRTE link is more than twice the value for the NPL-SYRTE link such that it is more sensitive to a violation of LI.”
Quote in the paperNot a substantial claimMay combine two claims.
Interpretationnone givenThe bound on alpha is purely limited by technical noise sources on the clock systems, which will improve in future comparisons.
“Moreover, this bound is purely limited by technical noise sources on the clock systems, which will improve in future comparisons.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
Study design and conductnone givenThe propagation noise in the fibers is actively compensated.
“The propagation noise in the fibers is actively compensated.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationA limit of |alpha| <= 8.4 x 10^-8 was found using 7Li+ ions prepared in a storage ring to 6.4% and 3.0% of the speed of light.
“A limit of jαj ≤ 8.4 × 10 -8 was found using 7 Li þ ions prepared in a storage ring to 6.4% and 3.0% of the speed of light [16].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [16] source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Study design and conductnone givenThe frequency counters at NPL, LPL, and SYRTE are synchronized to UTC(NPL), GPS time, and UTC(OP), respectively, with an accuracy well below 1 ms.
“The frequency counters at NPL, LPL, and SYRTE are synchronized to UTC(NPL), GPS time, and UTC(OP), respectively, with an accuracy well below 1 ms.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe Robertson-Mansouri-Sexl (RMS) kinematical framework contains only three parameters.
“In this Letter we use the Robertson-Mansouri-Sexl (RMS) kinematical framework [10][11][12][13] that contains only three parameters.”
Quote in the paperNot a substantial claim0 of 3 sources checkedProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductnone givenFor the combined data set C the correlation between both data sets is also taken into account in the covariance matrix.
“For the combined data set C the correlation between both data sets is also taken into account in the covariance matrix.”
Quote in the paperNot a substantial claimMay combine two claims.
Interpretationown dataA simulated sinusoid with a 1 day period leads to a complete degeneracy of all parameters with no unique solution, showing that the residual effect cannot be well represented by a simple sinusoidal model.
“and for (vi) to a complete degeneracy of all parameters with no unique solution, which shows that the residual effect cannot be well represented by a simple sinusoidal model, as parameters are completely degenerated with parameters from the LI violating model.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationWhen neglecting higher order RMS parameters, the constraint on the Lorentz-invariance-violating parameter alpha from Ref. [17] is |alpha| <~ 2.0 x 10^-8.
“When neglecting higher order RMS parameters, the constraint on the LI violating parameter is jαj ≲ 2.0 × 10 -8 .”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [17] source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationComparing resonance frequencies of optical clocks has led to new tests of fundamental physics, such as bounding the time variation of fundamental constants.
“Thanks to these unparalleled performances, comparing the resonance frequencies of optical clocks has led to new tests of fundamental physics, such as bounding the time variation of fundamental constants [7,8].”
Quote in the paperNot a substantial claim0 of 2 sources checkedMay combine two claims.
Interpretationown dataAlthough the 1 day^-1 signal could be interpreted as a violation of Lorentz invariance, a detailed analysis shows that this effect is probably due to temperature variations in the SYRTE clock laboratory.
“Although this signal could be interpreted as a violation of LI, a detailed analysis shows that this effect is probably due to temperature variations in the SYRTE clock laboratory.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductnone givenThe temporal correlation is taken into account in the MCMC method fit by using a nondiagonal covariance matrix.
“This temporal correlation is taken into account in the MCMC method fit by using a nondiagonal covariance matrix.”
Quote in the paperNot a substantial claimMay combine two claims.
PremisecitationThe connection between distant optical clocks achieved with phase-compensated optical fibers allows an unprecedented level of statistical resolution for comparison of remote atomic clocks, making such a test possible for the first time.
“The connection between these clocks, achieved with phase-compensated optical fibers, allows for an unprecedented level of statistical resolution for the comparison of remote atomic clocks [9], making such a test possible for the first time.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [9] source
Not checked in the free run.
Classified as probably not a substantial claim.
Study design and conductreasoningThe mean frequency offsets were removed from each comparison data subset because the analysis looks only for daily variations.
“The mean frequency offsets were removed from each comparison data subset as we are looking only for daily variations.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductnone givenThe relative frequency difference y_NPL-SYRTE between the NPL Sr clock and the SYRTE Sr clock is corrected from the term Delta_cl.
“The relative frequency difference y NPL-SYRTE between the NPL Sr clock and the SYRTE Sr clock is corrected from the term Δ cl .”
Quote in the paperNot a substantial claimMay combine two claims.
PremisecitationFirst-order tests in w/c based on comparison of clocks gave the best constraints on the Lorentz-invariance-violating parameter alpha until recently, with e.g. |alpha| <= 10^-6 obtained by comparing atomic clocks onboard GPS satellites with ground atomic clocks.
“Until recently, they gave the best constraints on the LI violating parameter α (see Ref. [14] for a review) with, e.g., jαj ≤ 10 -6 obtained by comparing atomic clocks' onboard GPS satellites with ground atomic clocks [15].”
Quote in the paperSubstantial claim0 of 2 sources checkedProbably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).
Interpretationnone givenThis work is the first of a new generation of tests of fundamental physics using optical clocks and fiber links.
“This work is the first of a new generation of tests of fundamental physics using optical clocks and fiber links.”
Quote in the paperNot a substantial claimMay combine two claims.
PremisecitationOptical clocks reach systematic uncertainties of a few 10^-18, which can be resolved after a few hours of measurement with optical lattice clocks based on trapped neutral atoms.
“They reach systematic uncertainties of a few 10 -18 , which can be resolved after a mere few hours of measurement with optical lattice clocks based on trapped neutral atoms [2][3][4][5][6].”
Quote in the paperSubstantial claim0 of 3 sources checkedProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe three classical Lorentz-invariance tests (Michelson-Morley, Kennedy-Thorndike, and Ives-Stillwell) are second-order tests because the Lorentz-invariance-violating signal depends on w^2/c^2.
“The three classical LI tests are the Michelson-Morley, Kennedy-Thorndike, and Ives-Stillwell experiments [10]; they are second-order tests as the LI violating signal depends on w 2 =c 2 [13].”
Quote in the paperNot a substantial claim0 of 2 sources checked
The authors state this as an assumption.
The Robertson-Mansouri-Sexl framework assumes the existence of a preferred frame Sigma where light propagates rectilinearly and isotropically in free space with constant speed c.
“It assumes the existence of a preferred frame Σ where light propagates rectilinearly and isotropically in free space with constant speed c.”
The authors state this as an assumption.
The preferred frame is taken as the rest frame of the cosmological microwave background (CMB).
“⃗w is the velocity of the Earth with respect to a preferred frame, taken as the rest frame of the cosmological microwave background (CMB).”
The authors state this as an assumption.
The terrestrial coordinates of the clocks are considered constant.
“They are obtained by transforming the terrestrial coordinates of the clocks, considered as constant, with the SOFA routines [29].”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Recent analysis of optical clock comparisons have included temporal variations.
“Recent analysis of optical clock comparisons have included temporal variations [130, 131].”
From Chronometric Geodesy: Methods and Applications (2019) · cites this paper as [131]
Recent analysis of optical clock comparisons already included temporal variations.
“Recent analysis of optical clock comparisons already included temporal variations [130, 131].”
From Chronometric Geodesy: Methods and Applications (2019) · cites this paper as [131]
These optical clocks can be used to explore geophysical phenomena, detect gravitational waves, test general relativity and search for dark matter.
“These optical clocks can further be used to explore geophysical phenomena 10 , detect gravitational waves 11 , test general relativity 12 and search for dark matter 13-17 .”
From Atomic clock performance enabling geodesy below the centimetre level (2018) · cites this paper as [12]
Cites
Ensemble samplers with affine invariance
Goodman, J. B., & Weare, J. (2010) · Communications in Applied Mathematics and Computational Science · doi:10.2140/camcos.2010.5.65 · Cited by 3,075 · see citing works
Lorentz-violating extension of the standard model
Colladay, D., & Kostelecký, V. A. (1998) · Physical Review D · doi:10.1103/physrevd.58.116002 · Cited by 2,403 · see citing works
Ludlow, A. D., Boyd, M. M., Ye, J., Peik, E., & Schmidt, P. O. (2015) · Reviews of Modern Physics · doi:10.1103/revmodphys.87.637 · Cited by 2,385 · see citing works
Colladay, D., & Kostelecký, V. A. (1997) · Physical Review D · doi:10.1103/physrevd.55.6760 · Cited by 1,779 · see citing works
Hinshaw, G. F., Weiland, J. L., Hill, R., Odegard, N., Larson, D., Bennett, C. L., Dunkley, J., Gold, B., Greason, M. R., Jarosik, N., et al. (2009) · The Astrophysical Journal Supplement Series · doi:10.1088/0067-0049/180/2/225 · Cited by 1,769 · see citing works
Modern Tests of Lorentz Invariance
Mattingly, D. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-5 · Cited by 1,061 · see citing works
Systematic evaluation of an atomic clock at 2 × 10−18 total uncertainty
Nicholson, T. L., Campbell, S. L., Hutson, R. B., Marti, G. E., Bloom, B. J., McNally, R. L., Zhang, W., Barrett, M. D., Safronova, M. S., Strouse, G. F., et al. (2015) · Nature Communications · doi:10.1038/ncomms7896 · Cited by 780 · see citing works
Signals for Lorentz violation in electrodynamics
Kostelecký, V. A., & Mewes, M. (2002) · Physical Review D · doi:10.1103/physrevd.66.056005 · Cited by 767 · see citing works
Cryogenic optical lattice clocks
Ushijima, I., Takamoto, M., Das, M., Ohkubo, T., & Katori, H. (2015) · Nature Photonics · doi:10.1038/nphoton.2015.5 · Cited by 627 · see citing works
Hunting for topological dark matter with atomic clocks
Derevianko, A., & Pospelov, M. (2014) · Nature Physics · doi:10.1038/nphys3137 · Cited by 522 · see citing works
Godun, R. M., Nisbet-Jones, P. B. R., Jones, J. M., King, S. A., Johnson, L. A. M., Margolis, H. S., Szymaniec, K., Lea, S. N., Bongs, K., & Gill, P. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.210801 · Cited by 468 · see citing works
Self-citationA clock network for geodesy and fundamental science
Lisdat, C., Grosche, G., Quintin, N., Shi, C., Raupach, S. M. F., Grebing, C., Nicolodi, D., Stefani, F., Al-Masoudi, A., Dörscher, S., et al. (2016) · Nature Communications · doi:10.1038/ncomms12443 · Cited by 460 · see citing works
Self-citationA test theory of special relativity: I. Simultaneity and clock synchronization
Mansouri, R., & Sexl, R. U. (1977) · General Relativity and Gravitation · doi:10.1007/bf00762634 · Cited by 440 · see citing works
Searching for dilaton dark matter with atomic clocks
Arvanitaki, A., Huang, J., & Van Tilburg, K. (2015) · Physical Review D · doi:10.1103/physrevd.91.015015 · Cited by 404 · see citing works
High-stability transfer of an optical frequency over long fiber-optic links
Williams, P. A., Swann, W. C., & Newbury, N. R. (2008) · Journal of the Optical Society of America B · doi:10.1364/josab.25.001284 · Cited by 386 · see citing works
Ultrastable optical clock with two cold-atom ensembles
Schioppo, M., Brown, R. C., McGrew, W. F., Hinkley, N., Fasano, R. J., Beloy, K., Yoon, T. H., Milani, G., Nicolodi, D., Sherman, J. A., et al. (2017) · Nature Photonics · doi:10.1038/nphoton.2016.231 · Cited by 385 · see citing works
Huntemann, N., Lipphardt, B., Tamm, C., Gerginov, V., Weyers, S., & Peik, E. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.210802 · Cited by 366 · see citing works
Postulate <i>versus</i> Observation in the Special Theory of Relativity
Robertson, H. P. (1949) · Reviews of Modern Physics · doi:10.1103/revmodphys.21.378 · Cited by 298 · see citing works
Experimental realization of an optical second with strontium lattice clocks
Le Targat, R., Lorini, L., Le Coq, Y., Zawada, M., Guéna, J., Abgrall, M., Gurov, M., Rosenbusch, P., Rovera, D. G., Nagórny, B., et al. (2013) · Nature Communications · doi:10.1038/ncomms3109 · Cited by 250 · see citing works
Self-citationWhat do we know about Lorentz invariance?
Tasson, J. D. (2014) · Reports on Progress in Physics · doi:10.1088/0034-4885/77/6/062901 · Cited by 203 · see citing works
A strontium lattice clock with 3 × 10<sup>−17</sup>inaccuracy and its frequency
Falke, S., Lemke, N., Grebing, C., Lipphardt, B., Weyers, S., Gerginov, V., Huntemann, N., Hagemann, C., Al-Masoudi, A., Häfner, S., et al. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/7/073023 · Cited by 182 · see citing works
Self-citationA test theory of special relativity: II. First order tests
Mansouri, R., & Sexl, R. U. (1977) · General Relativity and Gravitation · doi:10.1007/bf00762635 · Cited by 182 · see citing works
Optical frequency transfer via 146 km fiber link with 10^−19 relative accuracy
Grosche, G., Terra, O., Predehl, K., Holzwarth, R., Lipphardt, B., Vogt, F., Sterr, U., & Schnatz, H. (2009) · Optics Letters · doi:10.1364/ol.34.002270 · Cited by 161 · see citing works
Self-citationTest of relativistic time dilation with fast optical atomic clocks at different velocities
Reinhardt, S., Saathoff, G., Buhr, H., Carlson, L. A., Wolf, A., Schwalm, D., Karpuk, S., Novotny, C., Huber, G., Zimmermann, M., et al. (2007) · Nature Physics · doi:10.1038/nphys778 · Cited by 154 · see citing works
A test theory of special relativity: III. Second-order tests
Mansouri, R., & Sexl, R. U. (1977) · General Relativity and Gravitation · doi:10.1007/bf00759585 · Cited by 149 · see citing works
Realization of a timescale with an accurate optical lattice clock
Grebing, C., Al-Masoudi, A., Dörscher, S., Häfner, S., Gerginov, V., Weyers, S., Lipphardt, B., Riehle, F., Sterr, U., & Lisdat, C. (2016) · Optica · doi:10.1364/optica.3.000563 · Cited by 149 · see citing works
Self-citationSpectral purity transfer between optical wavelengths at the 10−18 level
Nicolodi, D., Argence, B., Zhang, W., Le Targat, R., Santarelli, G., & Le Coq, Y. (2014) · Nature Photonics · doi:10.1038/nphoton.2013.361 · Cited by 132 · see citing works
Self-citationTest of the isotropy of the one-way speed of light using hydrogen-maser frequency standards
Krisher, T. P., Maleki, L., Lutes, G. F., Primas, L. E., Logan, R. T., Anderson, J. D., & Will, C. M. (1990) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.42.731 · Cited by 130 · see citing works
Clock synchronization and isotropy of the one-way speed of light
Will, C. M. (1992) · Physical Review D · doi:10.1103/physrevd.45.403 · Cited by 122 · see citing works
Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock
Lodewyck, J., Bilicki, S., Bookjans, E., Robyr, J.-L., Shi, C., Vallet, G., Le Targat, R., Nicolodi, D., Le Coq, Y., Guéna, J., et al. (2016) · Metrologia · doi:10.1088/0026-1394/53/4/1123 · Cited by 102 · see citing works
Self-citationCascaded optical fiber link using the internet network for remote clocks comparison
Chiodo, N., Quintin, N., Stefani, F., Wiotte, F., Camisard, E., Chardonnet, C., Santarelli, G., Amy-Klein, A., Pottie, P.-E., & Lopez, O. (2015) · Optics Express · doi:10.1364/oe.23.033927 · Cited by 100 · see citing works
Self-citationSatellite test of special relativity using the global positioning system
Wolf, P., & Petit, G. (1997) · Physical Review A · doi:10.1103/physreva.56.4405 · Cited by 99 · see citing works
Noise and instability of an optical lattice clock
Al-Masoudi, A., Dörscher, S., Häfner, S., Sterr, U., & Lisdat, C. (2015) · Physical Review A · doi:10.1103/physreva.92.063814 · Cited by 84 · see citing works
Self-citationBotermann, B., Bing, D., Geppert, C., Gwinner, G., Hänsch, T. W., Huber, G., Karpuk, S., Krieger, A., Kühl, T., Nörtershäuser, W., et al. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.120405 · Cited by 82 · see citing works
Grosche, G. (2014) · Optics Letters · doi:10.1364/ol.39.002545 · Cited by 72 · see citing works
Self-citationTackling the limits of optical fiber links
Stefani, F., Lopez, O., Bercy, A., Lee, W.-K., Chardonnet, C., Santarelli, G., Pottie, P.-É., & Amy‐Klein, A. (2015) · Journal of the Optical Society of America B · doi:10.1364/josab.32.000787 · Cited by 63 · see citing works
Self-citationVoigt, C., Denker, H., & Timmen, L. (2016) · Metrologia · doi:10.1088/0026-1394/53/6/1365 · Cited by 50 · see citing works
Relativistic corrections for time and frequency transfer in optical fibres
Geršl, J., Delva, P., & Wolf, P. (2015) · Metrologia · doi:10.1088/0026-1394/52/4/552 · Cited by 40 · see citing works
Self-citationEvaluating the performance of the NPL femtosecond frequency combs: agreement at the 10 −21 level
Johnson, L. A. M., Gill, P., & Margolis, H. S. (2015) · Metrologia · doi:10.1088/0026-1394/52/1/62 · Cited by 40 · see citing works
Self-citationHybrid fiber links for accurate optical frequency comparison
Lee, W.-K., Stefani, F., Bercy, A., Lopez, O., Amy‐Klein, A., & Pottie, P.-É. (2017) · Applied Physics B · doi:10.1007/s00340-017-6736-5 · Cited by 39 · see citing works
Self-citationA low maintenance Sr optical lattice clock
Hill, I. R., Hobson, R., Bowden, W., Bridge, E. M., Donnellan, S., Curtis, E. A., & Gill, P. (2016) · Journal of Physics Conference Series · doi:10.1088/1742-6596/723/1/012019 · Cited by 37 · see citing works
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
Atomic clock performance enabling geodesy below the centimetre level
McGrew, W. F., Zhang, X., Fasano, R. J., Schäffer, S. A., Beloy, K., Nicolodi, D., Brown, R. C., Hinkley, N., Milani, G., Schioppo, M., et al. (2018) · Nature · doi:10.1038/s41586-018-0738-2 · Cited by 727 · see citing works
Demonstration of 4.8 × 10−17 stability at 1 s for two independent optical clocks
Oelker, E., Hutson, R. B., Kennedy, C. J., Sonderhouse, L., Bothwell, T., Goban, A., Kedar, D., Sanner, C., Robinson, J. M., Marti, G. E., et al. (2019) · Nature Photonics · doi:10.1038/s41566-019-0493-4 · Cited by 475 · see citing works
Self-citationMehlstäubler, T. E., Grosche, G., Lisdat, C., Schmidt, P. O., & Denker, H. (2018) · Reports on Progress in Physics · doi:10.1088/1361-6633/aab409 · Cited by 263 · see citing works
Self-citationGravitational Redshift Test Using Eccentric <i>Galileo</i> Satellites
Delva, P., Puchades, N., Schönemann, E., Dilssner, F., Courde, C., Bertone, S., Gonzalez, F., Hees, A., Le Poncin-Lafitte, C., Meynadier, F., et al. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.231101 · Cited by 210 · see citing works
Self-citationOriglia, S., Pramod, M. S., Schiller, S., Singh, Y., Bongs, K., Schwarz, R., Al-Masoudi, A., Dörscher, S., Herbers, S., Häfner, S., et al. (2018) · Physical Review A · doi:10.1103/physreva.98.053443 · Cited by 142 · see citing works
Self-citationSchioppo, M., Kronjäger, J., Silva, A., Ilieva, R., Paterson, J. W., Baynham, C. F. A., Bowden, W., Hill, I. R., Hobson, R., Vianello, A., et al. (2022) · Nature Communications · doi:10.1038/s41467-021-27884-3 · Cited by 118 · see citing works
Self-citationCommon-clock very long baseline interferometry using a coherent optical fiber link
Clivati, C., Aiello, R., Bianco, G., Bortolotti, C., De Natale, P., Di Sarno, V., Maddaloni, P., Maccaferri, G., Mura, A., Negusini, M., et al. (2020) · Optica · doi:10.1364/optica.393356 · Cited by 99 · see citing works
Ohmae, N., Takamoto, M., Takahashi, Y., Kokubun, M., Araki, K., Hinton, A., Ushijima, I., Muramatsu, T., Furumiya, T., Sakai, Y., et al. (2021) · Advanced Quantum Technologies · doi:10.1002/qute.202100015 · Cited by 79 · see citing works
Intercontinental comparison of optical atomic clocks through very long baseline interferometry
Pizzocaro, M., Sekido, M., Takefuji, K., Ujihara, H., Hachisu, H., Nemitz, N., Tsutsumi, M., Kondo, T., Kawai, E., Ichikawa, R., et al. (2021) · Nature Physics · doi:10.1038/s41567-020-01038-6 · Cited by 64 · see citing works
Lattice-induced photon scattering in an optical lattice clock
Dörscher, S., Schwarz, R., Al-Masoudi, A., Falke, S., Sterr, U., & Lisdat, C. (2018) · Physical Review A · doi:10.1103/physreva.97.063419 · Cited by 60 · see citing works
Self-citationAn accurate and robust metrological network for coherent optical frequency dissemination
Cantin, E., Tønnes, M., Le Targat, R., Amy-Klein, A., Lopez, O., & Pottie, P.-E. (2021) · New Journal of Physics · doi:10.1088/1367-2630/abe79e · Cited by 59 · see citing works
Self-citationOptical frequency distribution using laser repeater stations with planar lightwave circuits
Akatsuka, T., Goh, T., Imai, H., Oguri, K., Ishizawa, A., Ushijima, I., Ohmae, N., Takamoto, M., Katori, H., Hashimoto, T., et al. (2020) · Optics Express · doi:10.1364/oe.383526 · Cited by 55 · see citing works
Optical frequency transfer over submarine fiber links
Clivati, C., Tampellini, A., Mura, A., Levi, F., Marra, G., Galea, P., Xuereb, A., & Calonico, D. (2018) · Optica · doi:10.1364/optica.5.000893 · Cited by 55 · see citing works
Self-citationHuang, Y., Zhang, H., Zhang, B., Hao, Y., Guan, H., Zeng, M., Chen, Q., Lin, Y., Wang, Y., Cao, S., et al. (2020) · Physical Review A · doi:10.1103/physreva.102.050802 · Cited by 52 · see citing works
Studying the fundamental limit of optical fiber links to the 10<sup>−21</sup> level
Xu, D., Lee, W.-K., Stefani, F., Lopez, O., Amy-Klein, A., & Pottie, P.-E. (2018) · Optics Express · doi:10.1364/oe.26.009515 · Cited by 35 · see citing works
Self-citationChronometric Geodesy: Methods and Applications
Delva, P., Denker, H., & Lion, G. (2019) · Fundamental Theories of Physics · doi:10.1007/978-3-030-11500-5_2 · Cited by 28 · see citing works
Self-citationReciprocity of propagation in optical fiber links demonstrated to 10<sup>−21</sup>
Xu, D., Delva, P., Lopez, O., Amy-Klein, A., & Pottie, P.-E. (2019) · Optics Express · doi:10.1364/oe.27.036965 · Cited by 15 · see citing works
Self-citationLaboratory demonstration of geopotential measurement using transportable optical clocks
Liu, D.-X., Cao, J., Yuan, J.-B., Cui, K.-F., Yuan, Y., Zhang, P., Chao, S.-J., Shu, H.-L., & Huang, X.-R. (2023) · Chinese Physics B · doi:10.1088/1674-1056/ac6337 · Cited by 10 · see citing works
- Authors
- Delva, P., Lodewyck, J., Bilicki, S., Bookjans, E., Vallet, G., Le Targat, R., Pottie, P.-E., Guerlin, C., Meynadier, F., Le Poncin-Lafitte, C., Lopez, O., Amy-Klein, A., Lee, W.-K., Quintin, N., Lisdat, C., Al-Masoudi, A., Dörscher, S., Grebing, C., Grosche, G., Kuhl, A., Raupach, S., Sterr, U., Hill, I. R., Hobson, R., Bowden, W., Kronjäger, J., Marra, G., Rolland, A., Baynes, F. N., Margolis, H. S., & Gill, P.
- Affiliations
- Centre National de la Recherche Scientifique (FR)
- Physikalisch-Technische Bundesanstalt (DE)
- National Physical Laboratory (GB)
- ORCID
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2017-06-02
- Volume
- 118
- Issue
- 22
- Pages
- 221102-221102
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2595844539
- Cited by
- 227
- References
- 41
- Citations by year
- 2026: 14 · 2025: 21 · 2024: 19 · 2023: 26 · 2022: 27 · 2021: 19 · 2020: 33 · 2019: 31 · 2018: 26 · 2017: 11
- FWCI
- 13.68
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion, other-oa)
- HAL (submittedVersion)
- Adelaide Research & Scholarship (AR&S) (University of Adelaide) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Korea Research Institute of Standards and Science (16011007)
- National Research Council of Science and Technology (CAP-15-08-KRISS)
- Seventh Framework Programme (605243)
- Horizon 2020 Framework Programme
- Agence Nationale de la Recherche
- Institut National des Sciences de l’Univers, Centre National de la Recherche Scientifique
- Centre National d’Etudes Spatiales
- Conseil Régional, Île-de-France
- Deutsche Forschungsgemeinschaft (RTG 1729)
- European Metrology Research Programme
- European Metrology Programme for Innovation and Research (SIB02 NEAT-FT, SIB55 ITOC, 15SIB05 OFTEN, 15SIB03 OC18)
- UK National Measurement System: Quantum, Electromagnetics and Time Programme
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Frequency and Time Standards
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Computer Science › Computer Networks and Communications › Network Time Synchronization Technologies
- Keywords
- special relativity tests, time dilation, strontium optical lattice clock, optical fiber links, phase compensation, clock distribution
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-10.
Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-10.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review