The DOI matches its Crossref record; 14 of the 14 references it cites were found in a registry or an index.
Relativistic theory for time and frequency transfer to order $\vec {c}^{-3}$
Open accessAbstract
This paper is motivated by the current development of several space missions (e.g. ACES on International Space Station) that will use Earth-orbit laser cooled atomic clocks, providing a time-keeping accuracy of the order of 5 10-17 in fractional frequency. We show that to such accuracy, the theory of frequency transfer between Earth and Space must be extended from the currently known relativistic order (which has been needed in previous space experiments such as GP-A) to the next relativistic correction of order . We find that the frequency transfer includes the first and second-order Doppler contributions, the Einstein gravitational red-shift and, at the order , a mixture of these effects. As for the time transfer, it contains the standard Shapiro time delay, and we present an expression also including the first and second-order Sagnac corrections. Higher-order relativistic corrections, at least , are numerically negligible for time and frequency transfers in these experiments, being for instance of order 10-20 in fractional frequency. Particular attention is paid to the problem of the frequency transfer in the two-way experimental configuration. In this case we find a simple theoretical expression which extends the previous formula (Vessot et al. [CITE]) to the next order . In the Appendix we present the detailed proofs of all the formulas which will be needed in such experiments.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
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?
The same terms (dt_e/dτ_e and dt_r/dτ_r) appear also for different ways of frequency transfer such as satellite transfer.
“The same terms appear also for different ways of frequency transfer such as the satellite transfer (see e.g. [7]).”
From Relativistic corrections for time and frequency transfer in optical fibres (2015) · cites this paper as [7]
Analogous corrections appear also for satellite time transfer.
“Analogous corrections appear also for the satellite time transfer (see e.g. [7]).”
From Relativistic corrections for time and frequency transfer in optical fibres (2015) · cites this paper as [7]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Fourth test of general relativity
Shapiro, I. I. (1964) · Physical Review Letters · doi:10.1103/physrevlett.13.789 · Cited by 1,137
Test of Relativistic Gravitation with a Space-Borne Hydrogen Maser
Vessot, R. F. C., Levine, M. W., Mattison, E. M., Blomberg, E. L., Hoffman, T. E., Nystrom, G. U., Farrel, B. F., Decher, R., Eby, P. B., Baugher, C. R., et al. (1980) · Physical Review Letters · doi:10.1103/physrevlett.45.2081 · Cited by 649
Lorentz covariant theory of light propagation in gravitational fields of arbitrary-moving bodies
Kopeikin, S. M., & Schäfer, G. (1999) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.60.124002 · Cited by 189
High-accuracy measurement of the 87 Rb ground-state hyperfine splitting in an atomic fountain
Bize, S., Sortais, Y. R. P., Santos, M. S., Mandache, C., Clairon, A., & Salomon, C. (1999) · Europhysics Letters (EPL) · doi:10.1209/epl/i1999-00203-9 · Cited by 162
Self-citationPractical implications of relativity for a global coordinate time scale
Ashby, N., & Allan, D. W. (1979) · Radio Science · doi:10.1029/rs014i004p00649 · Cited by 85
T2L2 - Time transfer by Laser link: a new optical time transfer generation
Fridelance, P., Samain, É., & Veillet, C. (1997) · Experimental Astronomy · doi:10.1023/a:1007982512087 · Cited by 58
An orbiting clock experiment to determine the gravitational red shift
Kleppner, D., Vessot, R. F. C., & Ramsey, N. F. (1970) · Astrophysics and Space Science · doi:10.1007/bf00653616 · Cited by 42
Relativistic time scales in the solar system
Brumberg, V. A., & Kopeikin, S. M. (1990) · Celestial Mechanics and Dynamical Astronomy · doi:10.1007/bf00050674 · Cited by 36
Computation of the relativistic rate shift of a frequency standard
Petit, G., & Wolf, P. (1997) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/19.571812 · Cited by 23
Self-citationPoint Characteristics of Some Static Spherically Symmetric Space-times
Buchdahl, H. A. (1970) · Optica Acta International Journal of Optics · doi:10.1080/713818357 · Cited by 9
Perturbed Characteristic Functions: Application to the Linearized Gravitational Field
Buchdahl, H. A. (1979) · Australian Journal of Physics · doi:10.1071/ph790405 · Cited by 8
Feasibility of a second-order gravitational red-shift experiment
Jaffe, J., & Vessot, R. F. C. (1976) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.14.3294 · Cited by 7
Coordinate Time in the Vicinity of the Earth
Allan, D. W., & Ashby, N. (1986) · Relativity in Celestial Mechanics and Astrometry · doi:10.1007/978-94-009-4602-6_43 · Cited by 7
Relativistic effects in two-way time transfer via artificial satellites using laser technique
Klioner, S. A., & Fukushima, T. (1994) · Manuscripta geodetica. · doi:10.1007/bf03655459 · Cited by 2
Flagged first, then by citations
Research works printed but not linked: 11
- Ashby, N. 1998, IEEE International Frequency Control Symposium, 320
- Hetzel, P., & Soring, A. 1993, Proc. 7th European Frequency and Time Forum, Neuchâtel, 1993, Swiss Foundation for Research in Microtechnology, 125
- IAU transactions 1991, vol. XXIB, Proc. 21st Gen. Assembly Buenos Aires (Kluwer, Dordrecht, Boston, London)
- IAU 2000 transactions, in press; the complete resolutions can be found e.g. on http://danof.obspm.fr/iaucom19
- Klioner, 1993, Celest. Mech. Dyn. Astron., 53, 81
- Laurent, P., Lemonde P., Santarelli G., et al. 1999, in Proc. of the 14th Int. Conf. on Laser Spectrocopy, ed. R. Blatt, J. Eschner, D. Leibfried, & F. Schmidt-Kaler (World Scientific)
- Petit, 1994, A&A, 286, 971
- Salomon, C., & Veillet, C. 1996, in Proc. Symp. on Space Station Utilisation, ESA-SP 385, 295
- Veillet, C., & Fridelance, P. 1993, Proc. 7th European Frequency and Time Forum, Neuchâtel, 1993, Swiss Foundation for Research in Microtechnology, 637
- Will, C. M. 1981, Theory and Experiment in Gravitational Physics (Cambridge U. Press)
- Wolf, 1995, A&A, 304, 653
Cited by
Sorted by citations
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
Quantum tests of the Einstein Equivalence Principle with the STE–QUEST space mission
Altschul, B., Bailey, Q. G., Blanchet, L., Bongs, K., Bouyer, P., Cacciapuoti, L., Capozziello, S., Gaaloul, N., Giulini, D., Hartwig, J., et al. (2015) · Advances in Space Research · doi:10.1016/j.asr.2014.07.014 · Cited by 204
Self-citationBondarescu, R., Bondarescu, M., Hetényi, G., Boschi, L., Jetzer, P., & Balakrishna, J. (2012) · Geophysical Journal International · doi:10.1111/j.1365-246x.2012.05636.x · Cited by 71
Voigt, C., Denker, H., & Timmen, L. (2016) · Metrologia · doi:10.1088/0026-1394/53/6/1365 · Cited by 50
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
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
Shen, Z., Shen, W.-B., & Zhang, S. (2017) · Surveys in Geophysics · doi:10.1007/s10712-017-9414-6 · Cited by 25
Metadata
- Authors
- Blanchet, L., Salomon, C., Teyssandier, P., & Wolf, P.
- Affiliations
- Laboratoire Kastler Brossel (FR)
- Centre National de la Recherche Scientifique (FR)
- Bureau international des poids et mesures (FR)
- ORCID
- Wolf, P.
- Venue
- Astronomy & Astrophysics
- Publisher
- EDP Sciences
- Published
- 2001-04
- Volume
- 370
- Issue
- 1
- Pages
- 320-329
- ISSN
- 0004-6361 (ISSN-L)
- 1432-0746
- OpenAlex
- W2033895718
- Cited by
- 132
- References
- 14
- Citations by year
- 2026: 9 · 2025: 5 · 2024: 10 · 2023: 7 · 2022: 2 · 2021: 6 · 2020: 6 · 2019: 9 · 2018: 2 · 2017: 7 · 2016: 6 · 2015: 3 · 2014: 7 · 2013: 6 · 2012: 5
- FWCI
- 1.17
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Astronomy and Astrophysics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion)
- arXiv (Cornell University)
- 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 › Physics and Astronomy › Astronomy and Astrophysics › Pulsars and Gravitational Waves Research
- Keywords
- relativistic corrections, frequency transfer, time transfer, Doppler shift, gravitational redshift, Shapiro delay, Sagnac effect, adverse childhood experiences
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.
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
