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Underground test of gravity-related wave function collapse

Nature Physics volume 17, pages 74–78 (2021)Cite this article

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Abstract

Roger Penrose proposed that a spatial quantum superposition collapses as a back-reaction from spacetime, which is curved in different ways by each branch of the superposition. In this sense, one speaks of gravity-related wave function collapse. He also provided a heuristic formula to compute the decay time of the superposition—similar to that suggested earlier by Lajos Diósi, hence the name Diósi–Penrose model. The collapse depends on the effective size of the mass density of particles in the superposition, and is random: this randomness shows up as a diffusion of the particles’ motion, resulting, if charged, in the emission of radiation. Here, we compute the radiation emission rate, which is faint but detectable. We then report the results of a dedicated experiment at the Gran Sasso underground laboratory to measure this radiation emission rate. Our result sets a lower bound on the effective size of the mass density of nuclei, which is about three orders of magnitude larger than previous bounds. This rules out the natural parameter-free version of the Diósi–Penrose model.

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Fig. 1: The Diósi–Penrose (DP) model of gravity-related wave function collapse.
Fig. 2: Schematic representation of the experimental set-up.
Fig. 3: Measured radiation spectrum.
Fig. 4: Comparison between the measured and the simulated background spectra.
Fig. 5: Lower bounds on the spatial cutoff R0 of the DP model.

Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The MC simulation is based on Geant4 code, which is freely accessible at http://geant4.web.cern.ch/support/download. Experimental details used within the simulation code as part of this study are protected by a non-disclosure agreement with the manufacturing company, but the results of the simulation are available for this paper.

References

  1. Schrödinger, E. Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 823–828 (1935).

    Article  ADS  MATH  Google Scholar 

  2. Leggett, A. J. Macroscopic quantum systems and the quantum theory of measurement. Prog. Theor. Phys. Suppl. 69, 80–100 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  3. Weinberg, S. Precision tests of quantum mechanics. Phys. Rev. Lett. 62, 485–488 (1989).

    Article  ADS  Google Scholar 

  4. Bell, J. S. Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy (Cambridge Univ. Press, 2004).

  5. Ghirardi, G. C., Rimini, A. & Weber, T. Unified dynamics for microscopic and macroscopic systems. Phys. Rev. D 34, 470–491 (1986).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Adler, S. L. Quantum Theory as an Emergent Phenomenon: the Statistical Mechanics of Matrix Models as the Precursor of Quantum Field Theory (Cambridge Univ. Press, 2004).

  7. Weinberg, S. Collapse of the state vector. Phys. Rev. A 85, 062116 (2012).

    Article  ADS  Google Scholar 

  8. Ghirardi, G. C., Pearle, P. & Rimini, A. Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles. Phys. Rev. A 42, 78–89 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  9. Bassi, A. & Ghirardi, G. Dynamical reduction models. Phys. Rep. 379, 257–426 (2003).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. 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).

    Article  ADS  Google Scholar 

  11. Arndt, M. & Hornberger, K. Testing the limits of quantum mechanical superpositions. Nat. Phys. 10, 271–277 (2014).

    Article  Google Scholar 

  12. Feynman, R. Feynman Lectures on Gravitation (CRC Press, 2018).

  13. Penrose, R. & Mermin, N. D. The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics (Oxford Univ. Press, 1990).

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Penrose, R. On the gravitization of quantum mechanics 1: Quantum state reduction. Found. Phys. 44, 557–575 (2014).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Howl, R., Penrose, R. & Fuentes, I. Exploring the unification of quantum theory and general relativity with a Bose–Einstein condensate. New J. Phys. 21, 043047 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  17. Diósi, L. A universal master equation for the gravitational violation of quantum mechanics. Phys. Lett. A 120, 377–381 (1987).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  19. Ghirardi, G., Grassi, R. & Rimini, A. Continuous-spontaneous-reduction model involving gravity. Phys. Rev. A 42, 1057–1064 (1990).

    Article  ADS  Google Scholar 

  20. Diósi, L. Gravity-related wave function collapse: mass density resolution. J. Phys. Conf. Ser. 442, 012001 (2013).

  21. Diósi, L. Gravitation and quantum-mechanical localization of macro-objects. Phys. Lett. A 105, 199–202 (1984).

    Article  Google Scholar 

  22. Bahrami, M., Großardt, A., Donadi, S. & Bassi, A. The Schrödinger–Newton equation and its foundations. New J. Phys. 16, 115007 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  23. Salart, D., Baas, A., van Houwelingen, J. A., Gisin, N. & Zbinden, H. Spacelike separation in a Bell test assuming gravitationally induced collapses. Phys. Rev. Lett. 100, 220404 (2008).

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  25. Kovachy, T. et al. Quantum superposition at the half-metre scale. Nature 528, 530–533 (2015).

    Article  ADS  Google Scholar 

  26. Fein, Y. Y. et al. Quantum superposition of molecules beyond 25 kDa. Nat. Phys. 15, 1242–1245 (2019).

    Article  Google Scholar 

  27. Lee, K. C. et al. Entangling macroscopic diamonds at room temperature. Science 334, 1253–1256 (2011).

    Article  ADS  Google Scholar 

  28. Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011).

    Article  ADS  Google Scholar 

  29. Teufel, J. et al. Sideband cooling of micromechanical motion to the quantum ground state. Nature 475, 359–363 (2011).

    Article  ADS  Google Scholar 

  30. Wollman, E. E. et al. Quantum squeezing of motion in a mechanical resonator. Science 349, 952–955 (2015).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. Jain, V. et al. Direct measurement of photon recoil from a levitated nanoparticle. Phys. Rev. Lett. 116, 243601 (2016).

    Article  ADS  Google Scholar 

  32. Hong, S. et al. Hanbury Brown and Twiss interferometry of single phonons from an optomechanical resonator. Science 358, 203–206 (2017).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Vovrosh, J. et al. Parametric feedback cooling of levitated optomechanics in a parabolic mirror trap. J. Opt. Soc. Am. B 34, 1421–1428 (2017).

    Article  ADS  Google Scholar 

  34. Riedinger, R. et al. Remote quantum entanglement between two micromechanical oscillators. Nature 556, 473–477 (2018).

    Article  ADS  Google Scholar 

  35. Bahrami, M., Smirne, A. & Bassi, A. Role of gravity in the collapse of a wave function: a probe into the Diósi–Penrose model. Phys. Rev. A 90, 062105 (2014).

    Article  ADS  Google Scholar 

  36. Helou, B., Slagmolen, B., McClelland, D. E. & Chen, Y. LISA Pathfinder appreciably constrains collapse models. Phys. Rev. D 95, 084054 (2017).

    Article  ADS  Google Scholar 

  37. Diósi, L. & Lukács, B. Calculation of X-ray signals from Károlyházy hazy space-time. Phys. Lett. A 181, 366–368 (1993).

    Article  ADS  Google Scholar 

  38. Neder, H., Heusser, G. & Laubenstein, M. Low level γ-ray germanium-spectrometer to measure very low primordial radionuclide concentrations. Appl. Radiat. Isot. 53, 191–195 (2000).

    Article  Google Scholar 

  39. Heusser, G., Laubenstein, M. & Neder, H. Low-level germanium gamma-ray spectrometry at the μBq/kg level and future developments towards higher sensitivity. Radioact. Environ. 8, 495–510 (2006).

    Article  Google Scholar 

  40. Fu, Q. Spontaneous radiation of free electrons in a nonrelativistic collapse model. Phys. Rev. A 56, 1806–1811 (1997).

    Article  ADS  Google Scholar 

  41. Piscicchia, K. et al. CSL collapse model mapped with the spontaneous radiation. Entropy 19, 319 (2017).

    Article  ADS  Google Scholar 

  42. Tilloy, A. & Stace, T. M. Neutron star heating constraints on wave-function collapse models. Phys. Rev. Lett. 123, 080402 (2019).

    Article  ADS  Google Scholar 

  43. Debye, P. Interferenz von Röntgenstrahlen und Wärmebewegung. Ann. Phys. 348, 49–92 (1913).

    Article  Google Scholar 

  44. Waller, I. Zur Frage der Einwirkung der Wärmebewegung auf die Interferenz von Röntgenstrahlen. Z. Phys. 17, 398–408 (1923).

    Article  ADS  Google Scholar 

  45. Gao, H. & Peng, L.-M. Parameterization of the temperature dependence of the Debye–Waller factors. Acta Crystallogr. A 55, 926–932 (1999).

    Article  Google Scholar 

  46. Adler, S. L. & Bassi, A. Collapse models with non-white noises. J. Phys. A 40, 15083 (2007).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. Adler, S. L. & Bassi, A. Collapse models with non-white noises: II. Particle-density coupled noises. J. Phys. A 41, 395308 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  48. Gasbarri, G., Toroš, M., Donadi, S. & Bassi, A. Gravity induced wave function collapse. Phys. Rev. D 96, 104013 (2017).

    Article  ADS  MathSciNet  Google Scholar 

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

  50. Adler, S. L. & Ramazanoglu, F. M. Photon-emission rate from atomic systems in the CSL model. J. Phys. A 40, 13395 (2007).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  51. Adler, S. L., Bassi, A. & Donadi, S. On spontaneous photon emission in collapse models. J. Phys. A 46, 245304 (2013).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  52. Bassi, A. & Donadi, S. Spontaneous photon emission from a non-relativistic free charged particle in collapse models: a case study. Phys. Lett. A 378, 761–765 (2014).

    Article  ADS  MATH  Google Scholar 

  53. Donadi, S., Deckert, D.-A. & Bassi, A. On the spontaneous emission of electromagnetic radiation in the CSL model. Ann. Phys. 340, 70–86 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  54. Boswell, M. et al. Mage—a Geant4-based Monte Carlo application framework for low-background germanium experiments. IEEE Trans. Nucl. Sci. 58, 1212–1220 (2011).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank S. L. Adler, M. Arndt and H. Ulbricht for useful discussions and comments, and C. Capoccia, M. Carlesso and R. Del Grande for their help in preparing the figures. S.D. acknowledges support from The Foundation BLANCEFLOR Boncompagni Ludovisi, née Bildt, INFN and the Fetzer Franklin Fund. K.P. and C.C. acknowledge the support of the Centro Fermi—Museo Storico della Fisica e Centro Studi e Ricerche ‘Enrico Fermi’ (Open Problems in Quantum Mechanics project), the John Templeton Foundation (ID 58158) and FQXi. L.D. acknowledges the support of the National Research Development and Innovation Office of Hungary, grant nos. 2017-1.2.1-NKP-2017-00001 and K12435, and support by an FQXi minigrant. A.B. acknowledges support from the H2020 FET TEQ (grant no. 766900), the University of Trieste and INFN. All authors acknowledge support from the COST Action QTSpace (grant no. CA15220).

Author information

Authors and Affiliations

  1. Frankfurt Institute for Advanced Studies (FIAS), Frankfurt am Main, Germany

    Sandro Donadi

  2. Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Rome, Italy

    Kristian Piscicchia

  3. INFN, Laboratori Nazionali di Frascati, Frascati, Italy

    Kristian Piscicchia & Catalina Curceanu

  4. Wigner Research Centre for Physics, Budapest, Hungary

    Lajos Diósi

  5. INFN, Laboratori Nazionali del Gran Sasso, Assergi, Italy

    Matthias Laubenstein

  6. Department of Physics, University of Trieste, Trieste, Italy

    Angelo Bassi

  7. INFN, Sezione di Trieste, Trieste, Italy

    Angelo Bassi

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Contributions

S.D. and A.B. conceived and designed the theoretical aspects of the research; M.L., K.P. and C.C. designed the experimental part of the research; S.D. performed the theoretical calculations, with the assistance of A.B. and L.D.; M.L., K.P. and C.C. performed the experimental measurements; K.P. performed the data analysis, with the assistance of C.C., M.L. and L.D.; S.D., K.P. and A.B. prepared the manuscript and Supplementary Information in coordination with all authors.

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Correspondence to Sandro Donadi, Kristian Piscicchia or Angelo Bassi.

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Full theoretical and experimental analysis; Supplementary Figs. 1 and 2.

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Donadi, S., Piscicchia, K., Curceanu, C. et al. Underground test of gravity-related wave function collapse. Nat. Phys. 17, 74–78 (2021). https://doi.org/10.1038/s41567-020-1008-4

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