Universal decoherence due to gravitational time dilation


The physics of low-energy quantum systems is usually studied without explicit consideration of the background spacetime. Phenomena inherent to quantum theory in curved spacetime, such as Hawking radiation, are typically assumed to be relevant only for extreme physical conditions: at high energies and in strong gravitational fields. Here we consider low-energy quantum mechanics in the presence of gravitational time dilation and show that the latter leads to the decoherence of quantum superpositions. Time dilation induces a universal coupling between the internal degrees of freedom and the centre of mass of a composite particle. The resulting correlations lead to decoherence in the particle position, even without any external environment. We also show that the weak time dilation on Earth is already sufficient to affect micrometre-scale objects. Gravity can therefore account for the emergence of classicality and this effect could in principle be tested in future matter-wave experiments.

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Figure 1: Gravitational time dilation causes decoherence of composite quantum systems.
Figure 2: A composite particle in superposition will decohere owing to time dilation.
Figure 3: Decoherence due to gravitational time dilation as compared to decoherence due to emission of thermal radiation for sapphire microspheres.


  1. 1

    Colella, R., Overhauser, A. W. & Werner, S. A. Observation of gravitationally induced quantum interference. Phys. Rev. Lett. 34, 1472–1474 (1975).

    ADS  Article  Google Scholar 

  2. 2

    Chu, S. Laser manipulation of atoms and particles. Science 253, 861–866 (1991).

    ADS  Article  Google Scholar 

  3. 3

    Eibenberger, S., Gerlich, S., Arndt, M., Mayor, M. & Tüxen, J. Matter-wave interference with particles selected from a molecular library with masses exceeding 10,000 amu. Phys. Chem. Chem. Phys. 15, 14696 (2013).

    Article  Google Scholar 

  4. 4

    Giulini, D. et al. Decoherence and the Appearance of a Classical World in Quantum Theory (Springer-Verlag, 1996).

    Google Scholar 

  5. 5

    Zurek, W. H. Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715–775 (2003).

    ADS  MathSciNet  Article  Google Scholar 

  6. 6

    Caldeira, A. O. & Leggett, A. J. Path integral approach to quantum Brownian motion. Physica A 121, 587–616 (1983).

    ADS  MathSciNet  Article  Google Scholar 

  7. 7

    Joos, E. & Zeh, H. D. The emergence of classical properties through interaction with the environment. Z. Phys. B 59, 223–243 (1985).

    ADS  Article  Google Scholar 

  8. 8

    Hackermüller, L., Hornberger, K., Brezger, B., Zeilinger, A. & Arndt, M. Decoherence of matter waves by thermal emission of radiation. Nature 427, 711–714 (2004).

    ADS  Article  Google Scholar 

  9. 9

    Prokof’ev, N. V. & Stamp, P. C. E. Theory of the spin bath. Rep. Prog. Phys. 63, 669–726 (2000).

    ADS  Article  Google Scholar 

  10. 10

    Hanson, R., Dobrovitski, V. V., Feiguin, A. E., Gywat, O. & Awschalom, D. D. Coherent dynamics of a single spin interacting with an adjustable spin bath. Science 320, 352–355 (2008).

    ADS  Article  Google Scholar 

  11. 11

    Anastopoulos, C. Quantum theory of nonrelativistic particles interacting with gravity. Phys. Rev. D 54, 1600–1605 (1996).

    ADS  MathSciNet  Article  Google Scholar 

  12. 12

    Lamine, B., Hervé, R., Lambrecht, A. & Reynaud, S. Ultimate decoherence border for matter-wave interferometry. Phys. Rev. Lett. 96, 050405 (2006).

    ADS  Article  Google Scholar 

  13. 13

    Blencowe, M. P. Effective field theory approach to gravitationally induced decoherence. Phys. Rev. Lett. 111, 021302 (2013).

    ADS  Article  Google Scholar 

  14. 14

    Penrose, R. On gravity’s role in quantum state reduction. Gen. Relativ. Gravit. 28, 581–600 (1996).

    ADS  MathSciNet  Article  Google Scholar 

  15. 15

    Diósi, L. Models for universal reduction of macroscopic quantum fluctuations. Phys. Rev. A 40, 1165–1174 (1989).

    ADS  Article  Google Scholar 

  16. 16

    Bassi, A., Lochan, K., Satin, S., Singh, T. P. & Ulbricht, H. Models of wave-function collapse, underlying theories, and experimental tests. Rev. Mod. Phys. 85, 471–527 (2013).

    ADS  Article  Google Scholar 

  17. 17

    Einstein, A. Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes. Ann. Phys. 340, 898–908 (1911).

    Article  Google Scholar 

  18. 18

    Hafele, J. C. & Keating, R. E. Around-the-world atomic clocks: Predicted relativistic time gains. Science 177, 166–168 (1972).

    ADS  Article  Google Scholar 

  19. 19

    Chou, C. W., Hume, D. B., Rosenband, T. & Wineland, D. J. Optical clocks and relativity. Science 329, 1630–1633 (2010).

    ADS  Article  Google Scholar 

  20. 20

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

    ADS  Article  Google Scholar 

  21. 21

    Breuer, H-P. & Petruccione, F. The Theory of Open Quantum Systems (Oxford Univ. Press, 2002).

    Google Scholar 

  22. 22

    Einstein, A. & Infeld, L. The Evolution of Physics (Simon and Schuster, 1938).

    Google Scholar 

  23. 23

    Hogg, T. & Huberman, B. A. Recurrence phenomena in quantum dynamics. Phys. Rev. Lett. 48, 711–714 (1982).

    ADS  MathSciNet  Article  Google Scholar 

  24. 24

    Karolyhazy, F. Gravitation and quantum mechanics of macroscopic objects. Nuovo Cimento 42, 390–402 (1966).

    ADS  Article  Google Scholar 

  25. 25

    Zych, M., Costa, F., Pikovski, I., Ralph, T. C. & Brukner, Č. General relativistic effects in quantum interference of photons. Class. Quantum Gravity 29, 224010 (2012).

    ADS  MathSciNet  Article  Google Scholar 

  26. 26

    Ralph, T. C., Milburn, G. J. & Downes, T. Gravitationally induced decoherence of optical entanglement. Preprint at http://arxiv.org/abs/quant-ph/0609139 (2006).

  27. 27

    Kiesel, N. et al. Cavity cooling of an optically levitated submicron particle. Proc. Natl Acad. Sci. USA 110, 14180–14185 (2013).

    ADS  Article  Google Scholar 

  28. 28

    Asenbaum, P., Kuhn, S., Nimmrichter, S., Sezer, U. & Arndt, M. Cavity cooling of free Si nanospheres in high vacuum. Nature Commun. 4, 2743 (2013).

    ADS  Article  Google Scholar 

  29. 29

    Marshall, W., Simon, C., Penrose, R. & Bouwmeester, D. Towards quantum superpositions of a mirror. Phys. Rev. Lett. 91, 130401 (2003).

    ADS  MathSciNet  Article  Google Scholar 

  30. 30

    Lamb, J. W. Miscellaneous data on materials for millimetre and submillimetre optics. Int. J. Infrared Millim. Waves 17, 1997–2034 (1996).

    ADS  Article  Google Scholar 

  31. 31

    Lämmerzahl, C. A Hamilton operator for quantum optics in gravitational fields. Phys. Lett. A 203, 12–17 (1996).

    ADS  MathSciNet  Article  Google Scholar 

  32. 32

    Kiefer, C. & Singh, T. P. Quantum gravitational corrections to the functional Schrödinger equation. Phys. Rev. D 44, 1067–1076 (1991).

    ADS  MathSciNet  Article  Google Scholar 

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We thank M. Arndt, M. Aspelmeyer, L. Diosi and M. Vanner for discussions and S. Eibenberger for providing us with the illustration of the TPPF20 molecule. This work was supported by the Austrian Science Fund (FWF) through the doctoral program Complex Quantum Systems (CoQuS), the Vienna Center for Quantum Science and Technology (VCQ), the SFB FoQuS and the Individual Project 24621, by the Foundational Questions Institute (FQXi), the John Templeton Foundation, the Australian Research Council Centre of Excellence for Engineered Quantum Systems (grant number CE110001013), the European Commission through RAQUEL (No. 323970) and the COST Action MP1209.

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I.P., M.Z., F.C. and Č.B. contributed to all aspects of the research, with the leading input from I.P.

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Correspondence to Igor Pikovski.

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The authors declare no competing financial interests.

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Pikovski, I., Zych, M., Costa, F. et al. Universal decoherence due to gravitational time dilation. Nature Phys 11, 668–672 (2015). https://doi.org/10.1038/nphys3366

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