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Fundamental limits on clock precision from spacetime uncertainty in quantum collapse models

Nicola Bortolotti1,2,3,*, Catalina Curceanu3,4,†, Lajos Diósi5,6, Simone Manti3, and Kristian Piscicchia1,3

  • *Contact author: nicola.bortolotti@uniroma1.it
  • †Contact author: catalina.curceanu@lnf.infn.it
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Phys. Rev. Research 7, 043166 – Published 13 November, 2025

DOI: https://doi.org/10.1103/p6tj-lg8l

Abstract

Models of spontaneous wavefunction collapse explain the quantum-to-classical transition without invoking the von Neumann measurement postulate. Prominent frameworks, such as the Diósi-Penrose (DP) and continuous spontaneous localization (CSL) models, propose a continuous, spontaneous measurement of the mass density field of quantized matter. We show that this mechanism could link both models—not just DP—to fundamental uncertainties in Newtonian gravity. Despite their nonrelativistic nature, these models suggest an induced uncertainty in the flow of time due to fluctuations in the Newtonian potential. We calculate the ultimate limit on time uncertainty and demonstrate that the resulting clock-time uncertainty remains negligible for all contemporary timekeeping devices, including atomic clocks.

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References (39)

  1. E. P. Wigner, Remarks on the mind-body question, Philosophical Reflections and Syntheses (Springer, Berlin, Heidelberg, 1995), pp. 247–260.
  2. F. London and E. Bauer, The theory of observation in quantum mechanics, Quantum Theory and Measurement (Princeton University Press, 1983), pp. 217–259.
  3. H. P. Stapp, Mind, matter, and quantum mechanics, Found. Phys. 12, 363 (1982).
  4. D. J. Chalmers and K. J. McQueen, Consciousness and the collapse of the wave function, in Consciousness and Quantum Mechanics, edited by S. Gao (Oxford University Press, Oxford, 2022).
  5. G. C. Ghirardi, A. Rimini, and T. Weber, Unified dynamics for microscopic and macroscopic systems, Phys. Rev. D 34, 470 (1986).
  6. P. Pearle, Combining stochastic dynamical state-vector reduction with spontaneous localization, Phys. Rev. A 39, 2277 (1989).
  7. L. Diósi, Models for universal reduction of macroscopic quantum fluctuations, Phys. Rev. A 40, 1165 (1989).
  8. L. Diosi, A universal master equation for the gravitational violation of quantum mechanics, Phys. Lett. A 120, 377 (1987).
  9. G. Ghirardi, R. Grassi, and A. Rimini, Continuous-spontaneous-reduction model involving gravity, Phys. Rev. A 42, 1057 (1990).
  10. G. C. Ghirardi, P. Pearle, and A. Rimini, Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles, Phys. Rev. A 42, 78 (1990).
  11. R. Penrose, On gravity’s role in quantum state reduction, Gen. Relativ. Gravit. 28, 581 (1996).
  12. A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, Models of wave-function collapse, underlying theories, and experimental tests, Rev. Mod. Phys. 85, 471 (2013).
  13. M. Carlesso, S. Donadi, L. Ferialdi, M. Paternostro, H. Ulbricht, and A. Bassi, Present status and future challenges of non-interferometric tests of collapse models, Nat. Phys. 18, 243 (2022).
  14. F. Karolyhazy, Gravitation and quantum mechanics of macroscopic objects, Nuov. Cim. 42, 390 (1966).
  15. L. Diósi, Fundamental irreversibility: Planckian or Schrödinger-Newton? Entropy 20, 496 (2018).
  16. A. Tilloy and L. Diósi, Sourcing semiclassical gravity from spontaneously localized quantum matter, Phys. Rev. D 93, 024026 (2016).
  17. A. Tilloy and L. Diósi, Principle of least decoherence for Newtonian semiclassical gravity, Phys. Rev. D 96, 104045 (2017).
  18. K. Piscicchia, A. Bassi, C. Curceanu, R. Del Grande, S. Donadi, B. C. Hiesmayr, and A. Pichler, CSL collapse model mapped with the spontaneous radiation, Entropy 19, 319 (2017).
  19. P. Pearle and E. Squires, Bound state excitation, nucleon decay experiments and models of wave function collapse, Phys. Rev. Lett. 73, 1 (1994).
  20. L. Diósi, Relativistic theory for continuous measurement of quantum fields, Phys. Rev. A 42, 5086 (1990).
  21. G. Ghirardi, R. Grassi, and P. Pearle, Relativistic dynamical reduction models: general framework and examples, Found. Phys. 20, 1271 (1990).
  22. P. Pearle, Relativistic collapse model with tachyonic features, Phys. Rev. A 59, 80 (1999).
  23. J. Oppenheim, A postquantum theory of classical gravity? Phys. Rev. X 13, 041040 (2023).
  24. L. Diósi, Classical-quantum hybrid canonical dynamics and its difficulties with special and general relativity, Phys. Rev. D 110, 084052 (2024).
  25. S. Donadi, K. Piscicchia, R. Del Grande, C. Curceanu, M. Laubenstein, and A. Bassi, Novel CSL bounds from the noise-induced radiation emission from atoms, Eur. Phys. J. C 81, 773 (2021).
  26. I. Arnquist et al. (majorana Collaboration), Search for spontaneous radiation from wave function collapse in the majorana demonstrator, Phys. Rev. Lett. 129, 080401 (2022).
  27. K. Piscicchia, A. Porcelli, A. Bassi, M. Bazzi, M. Bragadireanu, M. Cargnelli, A. Clozza, L. De Paolis, R. Del Grande, M. Derakhshani et al., A novel approach to parameter determination of the continuous spontaneous localization collapse model, Entropy 25, 295 (2023).
  28. B. Helou, B. J. J. Slagmolen, D. E. McClelland, and Y. Chen, LISA pathfinder appreciably constrains collapse models, Phys. Rev. D 95, 084054 (2017).
  29. S. Donadi, K. Piscicchia, C. Curceanu, L. Diósi, M. Laubenstein, and A. Bassi, Underground test of gravity-related wave function collapse, Nat. Phys. 17, 74 (2021).
  30. S. L. Adler, A. Bassi, M. Carlesso, and A. Vinante, Testing continuous spontaneous localization with Fermi liquids, Phys. Rev. D 99, 103001 (2019).
  31. L. Diósi, Intrinsic time-uncertainties and decoherence: Comparison of 4 models, Braz. J. Phys. 35, 260 (2005).
  32. C. Zhang, T. Ooi, J. S. Higgins, J. F. Doyle, L. von der Wense, K. Beeks, A. Leitner, G. A. Kazakov, P. Li, P. G. Thirolf et al., Frequency ratio of the 229mTh nuclear isomeric transition and the Sr87 atomic clock, Nature (London) 633, 63 (2024).
  33. H. N. Hausser, J. Keller, T. Nordmann, N. M. Bhatt, J. Kiethe, H. Liu, I. M. Richter, M. von Boehn, J. Rahm, S. Weyers, E. Benkler, B. Lipphardt, S. Dörscher, K. Stahl, J. Klose, C. Lisdat, M. Filzinger, N. Huntemann, E. Peik, and T. E. Mehlstäubler, In+115−Yb+172 coulomb crystal clock with 2.5×10−18 systematic uncertainty, Phys. Rev. Lett. 134, 023201 (2025).
  34. E. Oelker, R. Hutson, C. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. Robinson, G. Marti et al., Demonstration of 4.8×10−17 stability at 1 s for two independent optical clocks, Nat. Photon. 13, 714 (2019).
  35. M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. Yoon, G. Milani, D. Nicolodi, J. Sherman et al., Ultrastable optical clock with two cold-atom ensembles, Nat. Photon. 11, 48 (2017).
  36. T. Bothwell, C. J. Kennedy, A. Aeppli, D. Kedar, J. M. Robinson, E. Oelker, A. Staron, and J. Ye, Resolving the gravitational redshift across a millimetre-scale atomic sample, Nature (London) 602, 420 (2022).
  37. G. Hobbs, L. Guo, R. Caballero, W. Coles, K. Lee, R. Manchester, D. Reardon, D. Matsakis, M. Tong, Z. Arzoumanian et al., A pulsar-based time-scale from the International Pulsar Timing Array, Mon. Not. R. Astron. Soc. 491, 5951 (2020).
  38. A. Rodin and V. Fedorova, Generalized three-cornered hat method and its application for the construction of an ensemble pulsar time scale, Astron. Lett. 48, 321 (2022).
  39. Y. Dong-shan, G. Yu-ping, and Z. Shu-hong, Ensemble pulsar time scale, Chin. Astron. Astrophys. 41, 430 (2017).

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Phys. Rev. Research 7, 043166– Published 13 November, 2025
  • Received 8 April 2025
  • Accepted 31 July 2025
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