Geodetic methods to determine the relativistic redshift at the level of 10 - 18 in the context of international timescales: a review and practical results

Research output: Contribution to journalArticleResearchpeer review

Authors

  • Heiner Denker
  • Ludger Timmen
  • Christian Voigt
  • Stefan Weyers
  • Ekkehard Peik
  • Helen S. Margolis
  • Pacôme Delva
  • Peter Wolf
  • Gérard Petit

Research Organisations

External Research Organisations

  • National Metrology Institute of Germany (PTB)
  • National Physical Laboratory (NPL)
  • Observatoire de Paris (OBSPARIS)
  • International Bureau of Weights and Measures
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Details

Original languageEnglish
Pages (from-to)487-516
Number of pages30
JournalJournal of geodesy
Volume92
Issue number5
Early online date12 Dec 2017
Publication statusPublished - May 2018

Abstract

The frequency stability and uncertainty of the latest generation of optical atomic clocks is now approaching the one part in 10 18 level. Comparisons between earthbound clocks at rest must account for the relativistic redshift of the clock frequencies, which is proportional to the corresponding gravity (gravitational plus centrifugal) potential difference. For contributions to international timescales, the relativistic redshift correction must be computed with respect to a conventional zero potential value in order to be consistent with the definition of Terrestrial Time. To benefit fully from the uncertainty of the optical clocks, the gravity potential must be determined with an accuracy of about 0.1m2s-2, equivalent to about 0.01 m in height. This contribution focuses on the static part of the gravity field, assuming that temporal variations are accounted for separately by appropriate reductions. Two geodetic approaches are investigated for the derivation of gravity potential values: geometric levelling and the Global Navigation Satellite Systems (GNSS)/geoid approach. Geometric levelling gives potential differences with millimetre uncertainty over shorter distances (several kilometres), but is susceptible to systematic errors at the decimetre level over large distances. The GNSS/geoid approach gives absolute gravity potential values, but with an uncertainty corresponding to about 2 cm in height. For large distances, the GNSS/geoid approach should therefore be better than geometric levelling. This is demonstrated by the results from practical investigations related to three clock sites in Germany and one in France. The estimated uncertainty for the relativistic redshift correction at each site is about 2 × 10 - 18.

Keywords

    Caesium and optical atomic clocks, Chronometric levelling, International timescales, Relativistic geodesy, Relativistic redshift, Terrestrial Time, Zero level reference gravity potential

ASJC Scopus subject areas

Cite this

Geodetic methods to determine the relativistic redshift at the level of 10 - 18 in the context of international timescales: a review and practical results. / Denker, Heiner; Timmen, Ludger; Voigt, Christian et al.
In: Journal of geodesy, Vol. 92, No. 5, 05.2018, p. 487-516.

Research output: Contribution to journalArticleResearchpeer review

Denker H, Timmen L, Voigt C, Weyers S, Peik E, Margolis HS et al. Geodetic methods to determine the relativistic redshift at the level of 10 - 18 in the context of international timescales: a review and practical results. Journal of geodesy. 2018 May;92(5):487-516. Epub 2017 Dec 12. doi: 10.1007/s00190-017-1075-1
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title = "Geodetic methods to determine the relativistic redshift at the level of 10 - 18 in the context of international timescales: a review and practical results",
abstract = "The frequency stability and uncertainty of the latest generation of optical atomic clocks is now approaching the one part in 10 18 level. Comparisons between earthbound clocks at rest must account for the relativistic redshift of the clock frequencies, which is proportional to the corresponding gravity (gravitational plus centrifugal) potential difference. For contributions to international timescales, the relativistic redshift correction must be computed with respect to a conventional zero potential value in order to be consistent with the definition of Terrestrial Time. To benefit fully from the uncertainty of the optical clocks, the gravity potential must be determined with an accuracy of about 0.1m2s-2, equivalent to about 0.01 m in height. This contribution focuses on the static part of the gravity field, assuming that temporal variations are accounted for separately by appropriate reductions. Two geodetic approaches are investigated for the derivation of gravity potential values: geometric levelling and the Global Navigation Satellite Systems (GNSS)/geoid approach. Geometric levelling gives potential differences with millimetre uncertainty over shorter distances (several kilometres), but is susceptible to systematic errors at the decimetre level over large distances. The GNSS/geoid approach gives absolute gravity potential values, but with an uncertainty corresponding to about 2 cm in height. For large distances, the GNSS/geoid approach should therefore be better than geometric levelling. This is demonstrated by the results from practical investigations related to three clock sites in Germany and one in France. The estimated uncertainty for the relativistic redshift correction at each site is about 2 × 10 - 18.",
keywords = "Caesium and optical atomic clocks, Chronometric levelling, International timescales, Relativistic geodesy, Relativistic redshift, Terrestrial Time, Zero level reference gravity potential",
author = "Heiner Denker and Ludger Timmen and Christian Voigt and Stefan Weyers and Ekkehard Peik and Margolis, {Helen S.} and Pac{\^o}me Delva and Peter Wolf and G{\'e}rard Petit",
note = "Funding Information: Acknowledgements The authors would like to thank Thomas Udem, Ronald Holzwarth, and Arthur Matveev (Max-Planck-Institut f{\"u}r Quan-tenoptik, MPQ, Garching, Germany) for their support and facilitating the access to the MPQ site, Christof V{\"o}lksen and Torsten Spohnholtz (Bayerische Akademie der Wissenschaften, Kommission f{\"u}r Erdmes-sung und Glaziologie, Munich, Germany) for carrying out the GNSS observations and the data processing for the MPQ site, Nico Linden-thal and Tobias Kersten (Leibniz Universit{\"a}t Hannover, LUH, Institut f{\"u}r Erdmessung, Hannover, Germany), Cord-Hinrich Jahn and Peter Lembrecht (Landesamt f{\"u}r Geoinformation und Landesvermessung Niedersachsen, LGLN, Landesvermessung und Geobasisinformation, Hannover, Germany) for corresponding GNSS work at LUH and PTB, and Martina Sacher (Bundesamt f{\"u}r Kartographie und Geod{\"a}sie, BKG, Leipzig, Germany) for providing information on the EVRF2007 heights and uncertainties, the associated height transformations, and a new adjustment of the UELN from 2017. This research was supported by the European Metrology Research Programme (EMRP) within the framework of a Researcher Excellence Grant associated with the Joint Research Project “International Timescales with Optical Clocks” (SIB55 ITOC), as well as the Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Centre 1128 “Relativistic Geodesy and Gravimetry with Quantum Sensors (geo-Q)”, project C04. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union. We also thank the reviewers for their valuable comments, which helped to improve the manuscript significantly.",
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T1 - Geodetic methods to determine the relativistic redshift at the level of 10 - 18 in the context of international timescales: a review and practical results

AU - Denker, Heiner

AU - Timmen, Ludger

AU - Voigt, Christian

AU - Weyers, Stefan

AU - Peik, Ekkehard

AU - Margolis, Helen S.

AU - Delva, Pacôme

AU - Wolf, Peter

AU - Petit, Gérard

N1 - Funding Information: Acknowledgements The authors would like to thank Thomas Udem, Ronald Holzwarth, and Arthur Matveev (Max-Planck-Institut für Quan-tenoptik, MPQ, Garching, Germany) for their support and facilitating the access to the MPQ site, Christof Völksen and Torsten Spohnholtz (Bayerische Akademie der Wissenschaften, Kommission für Erdmes-sung und Glaziologie, Munich, Germany) for carrying out the GNSS observations and the data processing for the MPQ site, Nico Linden-thal and Tobias Kersten (Leibniz Universität Hannover, LUH, Institut für Erdmessung, Hannover, Germany), Cord-Hinrich Jahn and Peter Lembrecht (Landesamt für Geoinformation und Landesvermessung Niedersachsen, LGLN, Landesvermessung und Geobasisinformation, Hannover, Germany) for corresponding GNSS work at LUH and PTB, and Martina Sacher (Bundesamt für Kartographie und Geodäsie, BKG, Leipzig, Germany) for providing information on the EVRF2007 heights and uncertainties, the associated height transformations, and a new adjustment of the UELN from 2017. This research was supported by the European Metrology Research Programme (EMRP) within the framework of a Researcher Excellence Grant associated with the Joint Research Project “International Timescales with Optical Clocks” (SIB55 ITOC), as well as the Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Centre 1128 “Relativistic Geodesy and Gravimetry with Quantum Sensors (geo-Q)”, project C04. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union. We also thank the reviewers for their valuable comments, which helped to improve the manuscript significantly.

PY - 2018/5

Y1 - 2018/5

N2 - The frequency stability and uncertainty of the latest generation of optical atomic clocks is now approaching the one part in 10 18 level. Comparisons between earthbound clocks at rest must account for the relativistic redshift of the clock frequencies, which is proportional to the corresponding gravity (gravitational plus centrifugal) potential difference. For contributions to international timescales, the relativistic redshift correction must be computed with respect to a conventional zero potential value in order to be consistent with the definition of Terrestrial Time. To benefit fully from the uncertainty of the optical clocks, the gravity potential must be determined with an accuracy of about 0.1m2s-2, equivalent to about 0.01 m in height. This contribution focuses on the static part of the gravity field, assuming that temporal variations are accounted for separately by appropriate reductions. Two geodetic approaches are investigated for the derivation of gravity potential values: geometric levelling and the Global Navigation Satellite Systems (GNSS)/geoid approach. Geometric levelling gives potential differences with millimetre uncertainty over shorter distances (several kilometres), but is susceptible to systematic errors at the decimetre level over large distances. The GNSS/geoid approach gives absolute gravity potential values, but with an uncertainty corresponding to about 2 cm in height. For large distances, the GNSS/geoid approach should therefore be better than geometric levelling. This is demonstrated by the results from practical investigations related to three clock sites in Germany and one in France. The estimated uncertainty for the relativistic redshift correction at each site is about 2 × 10 - 18.

AB - The frequency stability and uncertainty of the latest generation of optical atomic clocks is now approaching the one part in 10 18 level. Comparisons between earthbound clocks at rest must account for the relativistic redshift of the clock frequencies, which is proportional to the corresponding gravity (gravitational plus centrifugal) potential difference. For contributions to international timescales, the relativistic redshift correction must be computed with respect to a conventional zero potential value in order to be consistent with the definition of Terrestrial Time. To benefit fully from the uncertainty of the optical clocks, the gravity potential must be determined with an accuracy of about 0.1m2s-2, equivalent to about 0.01 m in height. This contribution focuses on the static part of the gravity field, assuming that temporal variations are accounted for separately by appropriate reductions. Two geodetic approaches are investigated for the derivation of gravity potential values: geometric levelling and the Global Navigation Satellite Systems (GNSS)/geoid approach. Geometric levelling gives potential differences with millimetre uncertainty over shorter distances (several kilometres), but is susceptible to systematic errors at the decimetre level over large distances. The GNSS/geoid approach gives absolute gravity potential values, but with an uncertainty corresponding to about 2 cm in height. For large distances, the GNSS/geoid approach should therefore be better than geometric levelling. This is demonstrated by the results from practical investigations related to three clock sites in Germany and one in France. The estimated uncertainty for the relativistic redshift correction at each site is about 2 × 10 - 18.

KW - Caesium and optical atomic clocks

KW - Chronometric levelling

KW - International timescales

KW - Relativistic geodesy

KW - Relativistic redshift

KW - Terrestrial Time

KW - Zero level reference gravity potential

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