Skip to main content

The effect of stationary axisymmetric spacetimes in interferometric visibility

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.


In this article, we consider a scenario in which a spin-1/2 quanton goes through a superposition of co-rotating and counter-rotating circular paths, which play the role of the paths of a Mach–Zehnder interferometer in a stationary and axisymmetric spacetime. Since the spin of the particle plays the role of a quantum clock, as the quanton moves in a superposed path it gets entangled with the momentum (or the path), and this will cause the interferometric visibility (or the internal quantum coherence) to drop, since, in stationary axisymmetric spacetimes there is a difference in proper time elapsed along the two trajectories. However, as we show here, the proper time of each path will couple to the corresponding local Wigner rotation, and the effect in the spin of the superposed particle will be a combination of both. Besides, we discuss a general framework to study the local Wigner rotations of spin-1/2 particles in general stationary axisymmetric spacetimes for circular orbits.

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

Fig. 1
Fig. 2
Fig. 3


  1. 1.

    Sagnac, G., Acad, C.R.: Sci. Paris, 157, 708 (1913), the English translation can be found in G. Rizzi and M.L. Ruggiero, Relativity in Rotating Frames, eds. (Kluwer Academic Publishers, Dordrecht, 2003)

  2. 2.

    Ruggiero, M.L., Tartaglia, A.: A Note on the Sagnac Effect and Current Terrestrial Experiments. Eur. Phys. J. Plus 129, 126 (2014)

    Article  Google Scholar 

  3. 3.

    Tartaglia, A.: Geometric Treatment of the Gravitomagnetic Clock Effect. Gen. Relativ. Gravit. 32, 1745 (2000)

    MathSciNet  Article  ADS  Google Scholar 

  4. 4.

    Mashhoon, B., Hehl, F.W., Theiss, D.S.: On the gravitational effects of rotating masses: the Thirring-Lense papers. Gen. Relativ. Gravit. 16, 711 (1984)

    MathSciNet  Article  ADS  Google Scholar 

  5. 5.

    Lucchesi, D., et al.: A 1% measurement of the gravitomagnetic field of the earth with laser-tracked satellites. Universe 6, 9 (2020)

    Article  Google Scholar 

  6. 6.

    Ciufolini, I., Pavlis, E.C.: A confirmation of the general relativistic prediction of the Lense-Thirring effect. Nature 431, 958 (2004)

    Article  ADS  Google Scholar 

  7. 7.

    Tartaglia, A., Ruggiero, M.L.: Angular momentum effects in Michelson–Morley type experiments. Gen. Relativ. Gravit. 34, 1371 (2002)

    MathSciNet  Article  ADS  Google Scholar 

  8. 8.

    Cohen, J.M., Mashhoon, B.: Standard clocks, interferometry, and gravitomagnetism. Phys. Lett. A 181, 353 (1993)

    Article  ADS  Google Scholar 

  9. 9.

    Gronwald, F., Gruber, E., Lichtenegger, H., Puntigam, R.A.: Gravity Probe C(lock): probing the gravitomagnetic field of the Earth by means of a clock experiment, arXiv:gr-qc/9712054 (1997)

  10. 10.

    Tartaglia, A.: Detection of the gravitomagnetic clock effect. Class. Quant. Grav. 17, 783 (2000)

    MathSciNet  Article  ADS  Google Scholar 

  11. 11.

    Tartaglia, A.: Influence of the angular momentum of astrophysical objects on light and clocks and related measurements. Class. Quant. Grav. 17, 2381 (2000)

    MathSciNet  Article  ADS  Google Scholar 

  12. 12.

    Bini, D., Jantzen, R.T., Mashhoon, B.: Gravitomagnetism and relative observer clock effects. Class. Quant. Grav. 18, 653 (2001)

    MathSciNet  Article  ADS  Google Scholar 

  13. 13.

    Faruque, S.B., Chayon, M.M.H., Moniruzzaman, M.: On the gravitomagnetic clock effect in quantum mechanics, arXiv:1502.06204 [gr-qc, physics:quant-ph] (2015)

  14. 14.

    Faruque, S.B.: A quantum analogy to the classical gravitomagnetic clock effect. Results Phys. 9, 1508 (2018)

    Article  ADS  Google Scholar 

  15. 15.

    Ruggiero, M.L., Tartaglia, A.: Test of gravitomagnetism with satellites around the Earth. Eur. Phys. J. Plus 134, 205 (2019)

    Article  Google Scholar 

  16. 16.

    Zych, M., Costa, F., Pikovski, I.: Quantum interferometric visibility as a witness of general relativistic proper time. Nat. Commun. 2, 505 (2011)

    Article  ADS  Google Scholar 

  17. 17.

    According with J. -M. Lévy-Leblond, the term ”quanton” was given by M. Bunge. The usefulness of this term is that one can refer to a generic quantum system without using words like particle or wave: J.-M. Lévy-Leblond, On the Nature of Quantons, Science and Education 12, 495 (2003)

  18. 18.

    Zych, M., Costa, F., Pikovski, I., Ralph, T.C.: General relativistic effects in quantum interference of photons. Class. Quant. Grav. 29, 224010 (2012)

    MathSciNet  Article  ADS  Google Scholar 

  19. 19.

    Brodutch, A., Gilchrist, A., Guff, T., Smith, A.R.H., Terno, D.R.: Post-Newtonian gravitational effects in quantum interferometry. Phys. Rev. D 91, 064041 (2015)

    Article  ADS  Google Scholar 

  20. 20.

    Zych, M., Pikovski, I., Costa, F., Brukner, Č: General relativistic effects in quantum interference of clocks. J. Phys. Conf. Ser. 723, 012044 (2016)

  21. 21.

    Papapetrou, A.: Spinning test-particles in general relativity. Proc. R. Soc. Lond. A Math. Phys. Sci. 209, 248 (1951)

    MathSciNet  MATH  ADS  Google Scholar 

  22. 22.

    Lanzagorta, M.: Quantum Information in Gravitational Fields. Morgan & Claypool Publishers, California (2014)

    Book  Google Scholar 

  23. 23.

    Terashima, H., Ueda, M.: Einstein-Podolsky-Rosen correlation in gravitational field. Phys. Rev. A 69, 032113 (2004)

    MathSciNet  Article  ADS  Google Scholar 

  24. 24.

    Wald, R.M.: General Relativity. University of Chicago Press, Chicago (1984)

    Book  Google Scholar 

  25. 25.

    Carroll, S.: Spacetime and Geometry: An Introduction to General Relativity. Addison-Wesley, Reading (2004)

    MATH  Google Scholar 

  26. 26.

    Nakahara, M.: Geometry, Topology and Physics. Institute of Physics Publishing, Bristol (1990)

    Book  Google Scholar 

  27. 27.

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

    Google Scholar 

  28. 28.

    Weinberg, S.: The Quantum Theory of Fields I. Cambridge University Press, Cambridge (1995)

    Book  Google Scholar 

  29. 29.

    Wigner, E.P.: On unitary representations of the inhomogeneous lorentz group. Ann. Math. 40, 149 (1939)

    MathSciNet  Article  ADS  Google Scholar 

  30. 30.

    Ohnuki, Y.: Unitary Representations of the Poincaré group and Relativistic Wave Equations. World Scientific, Singapore (1988)

    Book  Google Scholar 

  31. 31.

    Chadrasekhar, S.: The Mathematical Theory of Black Holes. Oxford University Press, New York (1983)

    Google Scholar 

  32. 32.

    Alsing, P.M., Stephenson Jr., G.J., Kilian, P.: Spin-induced non-geodesic motion, gyroscopic precession, Wigner rotation and EPR correlations of massive spin 1/2 particles in a gravitational field, arXiv:0902.1396 [quant-ph] (2009)

  33. 33.

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

    MathSciNet  Article  ADS  Google Scholar 

  34. 34.

    Teukolsky, S.A.: The Kerr metric. Class. Quant. Grav. 32, 124006 (2015)

    MathSciNet  Article  ADS  Google Scholar 

  35. 35.

    Hobson, M.P., Efstathiou, G., Lasenby, A.N.: General Relativity: An Introduction for Physicists. Cambridge University Press, Cambridge (2006)

    Book  Google Scholar 

  36. 36.

    Bardeen, J.M., Press, W.H., Teukolsky, S.A.: Rotating black holes: locally nonrotating frames, energy extraction, and scalar synchrotron radiation. Astrophys. J. 178, 347 (1972)

    Article  ADS  Google Scholar 

  37. 37.

    Lanzagorta, M., Salgado, M.: Detection of gravitational frame dragging using orbiting qubits. Class. Quant. Grav. 33, 105013 (2016)

    MathSciNet  Article  ADS  Google Scholar 

  38. 38.

    Bardeen, J.M.: Stability of circular orbits in stationary, axisymmetric space-times. Astrophys. J. 161, 103 (1970)

    MathSciNet  Article  ADS  Google Scholar 

  39. 39.

    Ryan, F.D.: Gravitational waves from the inspiral of a compact object into a massive, axisymmetric body with arbitrary multipole moments. Phys. Rev. D 52, 5707 (1995)

    Article  ADS  Google Scholar 

  40. 40.

    Esfahani, B.N.: Spin entanglement of two spin- particles in a classical gravitational field. J. Phys. A: Math. Theor. 43, 455305 (2010)

    MathSciNet  Article  Google Scholar 

  41. 41.

    Palmer, M.C., Takahashi, M., Westman, H.F.: Localized qubits in curved spacetimes. Ann. Phys. 327, 1078–1131 (2012)

    MathSciNet  Article  ADS  Google Scholar 

  42. 42.

    Tartaglia, A.: Gravitomagnetism, clocks and geometry. Eur. J. Phys. 22, 105 (2001)

    Article  Google Scholar 

  43. 43.

    Ryder, L.: Introduction to General Relativity. Cambridge University Press, Cambrige (2009)

    Book  Google Scholar 

  44. 44.

    Ruggiero, M.L., Tartaglia, A.: Gravitomagnetic effects, arXiv:gr-qc/0207065 (2002)

  45. 45.

    Basso, N.L.W., Maziero, J.: Complete complementarity relations in curved spacetimes. Phys. Rev. A 103, 032210 (2021)

    MathSciNet  Article  ADS  Google Scholar 

  46. 46.

    Koashi, M., Winter, A.: Monogamy of entanglement and other correlations. Phys. Rev. A 69, 022309 (2004)

    MathSciNet  Article  ADS  Google Scholar 

Download references


This work was supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), process 88882.427924/2019-01, and by the Instituto Nacional de Ciência e Tecnologia de Informação Quântica (INCT-IQ), process 465469/2014-0.

Author information



Corresponding author

Correspondence to Marcos L. W. Basso.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Basso, M.L.W., Maziero, J. The effect of stationary axisymmetric spacetimes in interferometric visibility. Gen Relativ Gravit 53, 70 (2021).

Download citation


  • Interferometric visibility
  • Stationary and axisymmetric spacetime
  • Local Wigner rotation