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Underground test of gravity-related wave function collapse


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 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.


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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




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.

Corresponding authors

Correspondence to Sandro Donadi or Kristian Piscicchia or Angelo Bassi.

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Supplementary information

Supplementary Information

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

Source data

Source Data Fig. 3

Source Data for Fig. 3.

Source Data Fig. 4

Source Data for Fig. 4.

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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).

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