Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

Dragging of inertial frames

Nature volume 449, pages 41–47 (2007)Cite this article

Abstract

The origin of inertia has intrigued scientists and philosophers for centuries. Inertial frames of reference permeate our daily life. The inertial and centrifugal forces, such as the pull and push that we feel when our vehicle accelerates, brakes and turns, arise because of changes in velocity relative to uniformly moving inertial frames. A classical interpretation ascribed these forces to acceleration relative to some absolute frame independent of the cosmological matter, whereas an opposite view related them to acceleration relative to all the masses and ‘fixed stars’ in the Universe. An echo and partial realization of the latter idea can be found in Einstein’s general theory of relativity, which predicts that a spinning mass will ‘drag’ inertial frames along with it. Here I review the recent measurements of frame dragging using satellites orbiting Earth.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Frame-dragging effects on clocks by a rotating mass.
Figure 2: Frame-dragging and the gravitomagnetic analogy of the general theory of relativity with electrodynamics.
Figure 3: The Lense–Thirring effect on the orbital plane of a test-particle.
Figure 4: The Lense–Thirring effect measured via the LAGEOS satellites 15, 16 in 2004 and its theoretical value predicted by the general theory of relativity.
Figure 5: Frame-dragging on the Gravity Probe B gyroscopes.

Similar content being viewed by others

References

  1. Misner, C. W., Thorne, K. S. & Wheeler, J. A. Gravitation (Freeman, San Francisco, 1973)

    Google Scholar 

  2. Weinberg, S. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972)

    Google Scholar 

  3. Ciufolini, I. & Wheeler, J. A. Gravitation and Inertia (Princeton Univ. Press, Princeton, New Jersey, 1995)

    Book  Google Scholar 

  4. Einstein, A. Letter to Ernst Mach. Zurich, 25 June 1913. In Gravitation (Misner, C. W., Thorne, K. S. & Wheeler, J. A.) 544 (Freeman, San Francisco, 1973)

    Google Scholar 

  5. Mach, E. Die Mechanik in Ihrer Entwicklung Historisch Kritisch-Dargestellt (Brockhaus, Leipzig, 1912); transl. The Science of Mechanics (Open Court, La Salle, Illinois, 1960)

    MATH  Google Scholar 

  6. Barbour, J.P. & fister, H. (eds) Mach's Principle. From Newton's Bucket to Quantum Gravity (Birkhauser, Boston, 1995)

    Google Scholar 

  7. Will, C. M. Was Einstein Right? Putting General Relativity to the Test 2nd edn (Basic Books, New York, 1993)

    Google Scholar 

  8. Will, C. M. Theory and Experiment in Gravitational Physics 2nd edn (Cambridge Univ. Press, Cambridge, UK, 1993)

    Book  Google Scholar 

  9. Will, C. M. The confrontation between general relativity and experiment. Living Rev. Rel. 9, 3 (2006); 〈http://www.livingreviews.org/lrr-2006-3〉

  10. Landau, L. D. & Lifshitz, E. M. The Classical Theory of Fields 3rd rev., English edn. (Pergamon, London, 1971)

    MATH  Google Scholar 

  11. Zeldovich & Novikov, I. D. Relativistic Astrophysics Vol. I Stars and Relativity (Univ. Chicago Press, Chicago, 1971)

    Google Scholar 

  12. Ciufolini, I. & Ricci, F. Time delay due to spin inside a rotating shell. Class. Quantum Grav. 19, 3875–3881 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  13. Thorne, K. S., Price, R. H. & Macdonald, D. A. The Membrane Paradigm (Yale Univ. Press, New Haven, 1986)

    MATH  Google Scholar 

  14. Schäfer, G. Gravitomagnetic effects. J. Gen. Rel. Grav. 36, 2223–2235 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  15. Ciufolini, I. & Pavlis, E. C. A confirmation of the general relativistic prediction of the Lense–Thirring effect. Nature 431, 958–960 (2004)

    Article  ADS  CAS  Google Scholar 

  16. Ciufolini, I., Pavlis, E. C. & Peron, R. Determination of frame-dragging using Earth gravity models from CHAMP and GRACE. New Astron. 11, 527–550 (2006)

    Article  ADS  Google Scholar 

  17. Ashtekar, A. Gravity, geometry and the quantum. In Proc. Albert Einstein Century Int. Conf. (Paris, 18–22 July 2005) (eds Alimi, J.-M. & Füzfa, A.) (American Institute of Physics, New York, 2006)

  18. Penrose, R. Gravitational collapse and space–time singularities. Phys. Rev. Lett. 14, 57–59 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  19. Hawking, S. W. & Ellis, G. F. R. The Large Structure of Space-time (Cambridge Univ. Press, Cambridge, 1973)

    Book  Google Scholar 

  20. de Sitter, W. On Einstein's Theory of Gravitation and its astronomical consequences. Mon. Not. R. Astron. Soc. 77, 155–184 (1916)

    Article  ADS  Google Scholar 

  21. Lense, J. & Thirring, H. Über den Einfluss der Eigenrotation der Zentralkorper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie. Phys. Z. 19, 156–163 (1918)

    MATH  Google Scholar 

  22. Bender, P. L. et al. The lunar laser ranging experiment. Science 182, 229–238 (1973)

    Article  ADS  CAS  Google Scholar 

  23. Williams, J. G., Turyshev, S. G. & Murphy, T. W. Improving LLR tests of gravitational theory. Int. J. Mod. Phys. D 13, 567–582 (2004)

    Article  ADS  Google Scholar 

  24. Cohen, S. C. & Dunn, P. J. LAGEOS scientific results. J. Geophys. Res. B 90, 9215–9438 (1985)

    Article  ADS  Google Scholar 

  25. Noomen, R., Klosko, S., Noll, C. & Pearlman, M. (eds) Toward Millimeter Accuracy. NASA CP 2003–212248 Proc. 13th Int. Laser Ranging Workshop (NASA Goddard, Greenbelt, Maryland, 2003)

  26. Ciufolini, I. Measurement of the Lense-Thirring drag on high-altitude laser-ranged artificial satellites. Phys. Rev. Lett. 56, 278–281 (1986)

    Article  ADS  CAS  Google Scholar 

  27. Ciufolini, I. On a new method to measure the gravitomagnetic field using two orbiting satellites. Nuovo Cimento. A 109, 1709–1720 (1996)

    Article  ADS  Google Scholar 

  28. Ciufolini, I. A comprehensive introduction to the LAGEOS gravitomagnetic experiment. Int. J. Mod. Phys. A 4, 3083–3145 (1989)

    Article  ADS  CAS  Google Scholar 

  29. Ries, J. C., Eanes, R. J., Watkins, M. M. & Tapley, B. NASA-ASI Study, Report Part A (CSR, Austin, 1989)

    Google Scholar 

  30. Ciufolini, I. et al. Italian Space Agency Phase A Report on LARES. (Italian Space Agency, ASI, Rome, 1998)

    Google Scholar 

  31. Rubincam, D. P. Drag on the LAGEOS satellite. J. Geophys. Res. B 95, 4881–4886 (1990)

    Article  ADS  Google Scholar 

  32. Lucchesi, D. M. Reassessment of the error modelling of non-gravitational perturbations on LAGEOS II and their impact in the Lense-Thirring derivation. Part II. Planet. Space Sci. 50, 1067–1100 (2002)

    Article  ADS  Google Scholar 

  33. Kaula, W. M. Theory of Satellite Geodesy (Blaisdell, Waltham, 1966)

    MATH  Google Scholar 

  34. Reigber, C. et al. An Earth gravity field model complete to degree and order 150 from GRACE: EIGENGRACE02S. J. Geodyn. 39, 1–10 (2005)

    Article  ADS  Google Scholar 

  35. Ciufolini, I., Pavlis, E. C., Chieppa, F., Fernandes-Vieira, E. & Perez-Mercader, J. Test of general relativity and measurement of the Lense–Thirring effect with two Earth satellites. Science 279, 2100–2103 (1998)

    Article  ADS  CAS  Google Scholar 

  36. Ciufolini, I., Chieppa, F., Lucchesi, D. & Vespe, F. Test of Lense-Thirring orbital shift due to spin. Class. Quantum Grav. 14, 2701–2726 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  37. Ries, J. C., Eanes, R. J., Tapley, B. D. & Peterson, G. E. Prospects for an improved Lense-Thirring test with SLR and the GRACE gravity mission. In Toward Millimeter Accuracy. Proc. 13th Int. Laser Ranging Workshop (eds Noomen, R., Klosko, S., Noll, C. & Pearlman, M.) Report NASA CP 2003–212248 (NASA Goddard, Greenbelt, Maryland, 2003)

  38. Pavlis, E. C. in Recent Developments in General Relativity (Genoa, 2000) (eds Cianci, R. et al.) 217–233 (Springer Italia, Milan, 2002)

    Book  Google Scholar 

  39. Reigber et al. GRACE orbit and gravity field recovery at GFZ Potsdam—first experiences and perspectives. Eos (Fall Meet. Suppl.) 83 (47), abstr. G12B–03. (2002)

  40. Tapley, B. D. The GRACE mission: status and performance assessment. Eos (Fall Meet. Suppl.) 83 (47), abstr. G12B–01. (2002)

  41. Ciufolini, I. et al. in Proc. First Intl School of Astrophysical Relativity “John Archibald Wheeler”: Frame-Dragging, Gravitational-Waves and Gravitational Tests (eds Ciufolini, I. & Matzner, R. A.) (Springer, in the press).

  42. Pugh, G. E. Proposal for a Satellite Test of the Coriolis Prediction of General Relativity. Weapons Systems Evaluation Group Research Memorandum N. 11 (The Pentagon, Washington, 1959)

    Google Scholar 

  43. Schiff, L. I. Motion of a gyroscope according to Einstein's Theory of Gravitation. Proc. Natl. Acad. Sci. 46, 871–882 (1960)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  44. Schiff, L. I. Possible new test of General Relativity Theory. Phys. Rev. Lett. 4, 215–217 (1960)

    Article  ADS  Google Scholar 

  45. Everitt, C. W. F. et al. Papers on the Stanford Relativity gyroscope experiment (NASA Gravity Probe B). Proc. SPIE 619, 29–165 (Society for Photo-Optical Instrumentation Engineers, Washington, 1986)

  46. Fitch, V. L. et al. Review of Gravity Probe B (National Academic Press, Washington DC, 1995)

    Google Scholar 

  47. Buchman, S., Everitt, C. W. F., Parkinson, B., Turneaure, J. P. & Keiser, G. M. Cryogenic gyroscopes for the relativity mission. Physica B 280, 497–498 (2000)

    Article  ADS  CAS  Google Scholar 

  48. Becker, R., Heller, G. & Sauter, F. Über die Stromverteilung in Einer Supraleitenden Kugel. Z. Phys. 85, 772–787 (1933)

    Article  ADS  Google Scholar 

  49. London, F. Superfluids Vol. 1 (Wiley, New York, 1950)

    MATH  Google Scholar 

  50. Muhlfelder, B., Keiser, G. M. & Turneaure, J. GP-B Experiment Error: A Work in Progress. (Stanford Univ., Stanford, April 2007); poster at 〈http://einstein.stanford.edu/content/aps_posters/ExperimentError.pdf〉

  51. Gill, D. K. & Buchman, S. Evidence for Patch Effect Forces On the Gravity Probe B Gyroscopes. (Stanford Univ., Stanford, April 2007); poster at 〈http://einstein.stanford.edu/content/aps_posters/EvidenceForPatchEffectForces.pdf〉

  52. Barker, B. M. & O’Connel, R. F. The gyroscope test of General Relativity. Nature 312, 314 (1984)

    Article  ADS  Google Scholar 

  53. Barker, B. M. & O’Connel, R. F. The gravitational interaction: spin, rotation, and quantum effects—a review. Gen. Rel. Grav. 11, 149–175 (1979)

    Article  ADS  Google Scholar 

  54. de Sitter, W. On Einstein's Theory of Gravitation and its Astronomical Consequences. Mon. Not. R. Astron. Soc. 76, 699–728 (1916)

    Article  ADS  Google Scholar 

  55. Ciufolini, I. Gravitomagnetism, frame-dragging and lunar laser ranging. Preprint at 〈http://xxx.lanl.gov/abs/0704.3338〉 (10 May, 2007)

  56. Ashby, N. & Shahid-Saless, B. Geodetic precession or dragging of inertial frames? Phys. Rev. D 42, 1118–1122 (1990)

    Article  ADS  CAS  Google Scholar 

  57. O’Connell, R. F. A note on frame dragging. Class. Quant. Grav. 22, 3815–3816 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  58. Williams, J. G., Turyshev, S. G. & Boggs, D. H. Progress in lunar laser ranging tests of relativistic gravity. Phys. Rev. Lett. 93, 261101 (2004)

    Article  ADS  Google Scholar 

  59. Williams, J. G., Newhall, X. X. & Dickey, J. O. Relativity parameters determined from lunar laser ranging. Phys. Rev. D 53, 6730–6739 (1996)

    Article  ADS  CAS  Google Scholar 

  60. Bertotti, B., Ciufolini, I. & Bender, P. L. New test of general relativity: measurement of de Sitter geodetic precession rate for lunar perigee. Phys. Rev. Lett. 58, 1062–1065 (1987)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  61. Weisberg, J. M. & Taylor, J. H. General relativistic geodetic spin precession in binary pulsar B1913+16: mapping the emission beam in two dimensions. Astrophys. J. 576, 942–949 (2002)

    Article  ADS  Google Scholar 

  62. Stairs, I. H., Thorsett, S. E. & Arzoumanian, Z. Measurement of gravitational spin-orbit coupling in a binary-pulsar system. Phys. Rev. Lett. 93, 141101 (2004)

    Article  ADS  CAS  Google Scholar 

  63. Murphy, T. W., Nordtvedt, K. & Turyshev, S. G. Gravitomagnetic influence on gyroscopes and on the lunar orbit. Phys. Rev. Lett. 98, 071102 (2007)

    Article  ADS  Google Scholar 

  64. Kopeikin, S. M. Comment on “The gravitomagnetic influence on gyroscopes and on the lunar orbit”. Phys. Rev. Lett. 98, 229001 (2007)

    Article  ADS  Google Scholar 

  65. Kopeikin, S. M. & Fomalont, E. B. Gravimagnetism, causality, and aberration of gravity in the gravitational light-ray deflection experiments. Gen. Rel. Grav. (in the press); preprint at 〈http://xxx.lanl.gov/abs/gr-qc/0510077〉 (2005)

  66. Will, C. M. Propagation speed of gravity and the relativistic time delay. Astrophys. J. 590, 683–690 (2003)

    Article  ADS  Google Scholar 

  67. Cui, W. et al. Evidence for frame-dragging around spinning black holes in X-ray binaries. Astrophys. J. 492, L53–L58 (1998)

    Article  ADS  CAS  Google Scholar 

  68. Hewish, A., Bell, S. J., Pilkington, J. D. H., Scott, P. F. & Collins, R. A. Observation of a rapidly pulsating radio source. Nature 217, 709–713 (1968)

    Article  ADS  Google Scholar 

  69. Stairs, I. H. Testing General Relativity with pulsar timing. Living Rev. Rel. 6, 5 (2003); 〈http://relativity.livingreviews.org/articles/lrr-2003-5/index.html〉

  70. Backer, D. C., Kulkami, S. R., Heiles, C., Davis, M. M. & Goss, W. M. A millisecond pulsar. Nature 300, 615–618 (1982)

    Article  ADS  Google Scholar 

  71. Hulse, R. A. & Taylor, J. H. Discovery of a pulsar in a binary system. Astrophys. J. 195, L51–L53 (1975)

    Article  ADS  Google Scholar 

  72. Kramer, M. et al. Tests of general relativity from timing the double pulsar. Science 314, 97–102 (2006)

    Article  ADS  CAS  Google Scholar 

  73. Nordtvedt, K. Existence of the gravitomagnetic interaction. Int. J. Theor. Phys. 27, 1395–1404 (1988)

    Article  CAS  Google Scholar 

  74. Riess, A. et al. Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009–1038 (1998)

    Article  ADS  Google Scholar 

  75. Perlmutter, S. et al. Measurements of Ω and Λ from 42 high-redshift supernovae. Astrophys. J. 517, 565–586 (1999)

    Article  ADS  Google Scholar 

  76. Perlmutter, S. Supernovae, dark energy, and the accelerating universe. Phys. Today 56, 53–59 (2003)

    Article  CAS  Google Scholar 

  77. Caldwell, R. R. Dark energy. Phys. World 17, 37–42 (2004)

    Article  Google Scholar 

  78. Adelberger, E., Heckel, B. & Hoyle, C. D. Testing the gravitational inverse-square law. Phys. World 18, 41–45 (2005)

    Article  Google Scholar 

  79. Amelino-Camelia, G., Ellis, J., Mavromatos, N. E., Nanopoulos, D. V. & Sarkar, S. Potential sensitivity of gamma-ray burster observations to wave dispersion in vacuo. Nature 393, 763–765 (1998)

    Article  ADS  CAS  Google Scholar 

  80. Dvali, G. Filtering gravity: modification at large distances? In Proc. Nobel Symp. 127 on String Theory and Cosmology (Sigtuna, Sweden, 2003) (eds Danielsson, U., Goobar, A. & Nilsson, B. ) (World Scientific, Singapore, 2005); also preprint at 〈http://arXiv.org/hep-th/0402130〉 (2004)

  81. Kerr, R. P. Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. 11, 237–238 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  82. Ciufolini, I. et al. NASA-ASI Study, Report Part B (ASI, Rome, 1989)

    Google Scholar 

Download references

Acknowledgements

I gratefully acknowledge the support of the Italian Space Agency and the comments of R. Matzner of the Centre for Relativity, University of Texas at Austin, I. Novikov of the Astro Space Centre, Lebedev Physical Institute Moscow and D. P. Rubincam of NASA-Goddard.

Author information

Authors and Affiliations

  1. University of Salento and INFN Sezione di Lecce, Via Monteroni, 78100 Lecce, Italy,

    Ignazio Ciufolini

Authors
  1. Ignazio Ciufolini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ignazio Ciufolini.

Ethics declarations

Competing interests

Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ciufolini, I. Dragging of inertial frames. Nature 449, 41–47 (2007). https://doi.org/10.1038/nature06071

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature06071

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing