The superposition principle is the cornerstone of quantum mechanics, leading to a variety of genuinely quantum effects. Whether the principle applies also to macroscopic systems or, instead, there is a progressive breakdown when moving to larger scales is a fundamental and still open question. Spontaneous wavefunction collapse models predict the latter option, thus questioning the universality of quantum mechanics. Technological advances allow to increasingly challenge collapse models and the quantum superposition principle, with a variety of different experiments. Among them, non-interferometric experiments proved to be the most effective in testing these models. We provide an overview of such experiments, including cold atoms, optomechanical systems, X-ray detection, bulk heating and comparisons with cosmological observations. We also discuss avenues for future dedicated experiments, which aim at further testing collapse models and the validity of quantum mechanics.
This is a preview of subscription content, access via your institution
Subscribe to Nature+
Get immediate online access to Nature and 55 other Nature journal
Subscribe to Journal
Get full journal access for 1 year
only $8.25 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Penrose, R. On gravity’s role in quantum state reduction. Gen. Relativ. Gravit. 28, 581–600 (1996).
Adler, S. Quantum Theory as an Emergent Phenomenon (Cambridge Univ. Press, 2004).
Leggett, A. J. The quantum measurement problem. Science 307, 871–872 (2005).
Weinberg, S. Collapse of the state vector. Phys. Rev. A 85, 062116 (2012).
Arndt, M. & Hornberger, K. Testing the limits of quantum mechanical superpositions. Nat. Phys. 10, 271–277 (2014).
Pearle, P. Combining stochastic dynamical state-vector reduction with spontaneous localization. Phys. Rev. A 39, 2277–2289 (1989).
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).
Diósi, L. A universal master equation for the gravitational violation of quantum mechanics. Phys. Lett. A 120, 377–381 (1987).
Gisin, N. Stochastic quantum dynamics and relativity. Helv. Phys. Acta 63, 363–371 (1989).
Arnold, L. Stochastic Differential Equations (John Wiley & Sons, 1971).
Pearle, P. & Squires, E. Bound state excitation, nucleon decay experiments and models of wave function collapse. Phys. Rev. Lett. 73, 1–5 (1994).
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).
Ghirardi, G. C., Rimini, A. & Weber, T. Unified dynamics for microscopic and macroscopic systems. Phys. Rev. D 34, 470–491 (1986).
Adler, S. L. Lower and upper bounds on CSL parameters from latent image formation and IGM heating. J. Phys. A 40, 2935–2957 (2007).
Ghirardi, G., Grassi, R. & Rimini, A. Continuous-spontaneous-reduction model involving gravity. Phys. Rev. A 42, 1057–1064 (1990).
Penrose, R. Wavefunction collapse as a real gravitational effect. In Mathematical Physics 2000, 266–282 (World Scientific, 2000).
Penrose, R. On the gravitization of quantum mechanics 1: quantum state reduction. Found. Phys. 44, 557–575 (2014).
Fein, Y. Y. et al. Quantum superposition of molecules beyond 25 kDa. Nat. Phys. 15, 1242–1245 (2019).
Gasbarri, G. et al. Testing the foundation of quantum physics in space via interferometric and non-interferometric experiments with mesoscopic nanoparticles. Commun. Phys. 4, 155 (2021).
Belenchia, A. et al. Test quantum mechanics in space—invest US$1billion. Nature 596, 32–34 (2021).
Marshall, W., Simon, C., Penrose, R. & Bouwmeester, D. Towards quantum superpositions of a mirror. Phys. Rev. Lett. 91, 130401 (2003).
Machluf, S., Japha, Y. & Folman, R. Coherent Stern–Gerlach momentum splitting on an atom chip. Nat. Commun. 4, 2424 (2013).
Bateman, J., Nimmrichter, S., Hornberger, K. & Ulbricht, H. Near-field interferometry of a free-falling nanoparticle from a point-like source. Nat. Commun. 5, 4788 (2014).
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).
Collett, B. & Pearle, P. Wavefunction collapse and random walk. Found. Phys. 33, 1495–1541 (2003).
Bahrami, M. Testing collapse models by a thermometer. Phys. Rev. A 97, 052118 (2018).
Adler, S. L. & Vinante, A. Bulk heating effects as tests for collapse models. Phys. Rev. A 97, 052119 (2018).
Alduino, C. et al. The projected background for the CUORE experiment. Eur. Phys. J. C 77, 543 (2017).
Mishra, R., Vinante, A. & Singh, T. P. Testing spontaneous collapse through bulk heating experiments: an estimate of the background noise. Phys. Rev. A 98, 052121 (2018).
Pobell, F. Matter and Methods at Low Temperatures Vol. 2 (Springer, 2007).
Laloë, F., Mullin, W. J. & Pearle, P. Heating of trapped ultracold atoms by collapse dynamics. Phys. Rev. A 90, 052119 (2014).
Bilardello, M., Donadi, S., Vinante, A. & Bassi, A. Bounds on collapse models from cold-atom experiments. Phys. A 462, 764–782 (2016).
Kovachy, T. et al. Matter wave lensing to picokelvin temperatures. Phys. Rev. Lett. 114, 143004 (2015).
Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).
Bahrami, M., Paternostro, M., Bassi, A. & Ulbricht, H. Proposal for a noninterferometric test of collapse models in optomechanical systems. Phys. Rev. Lett. 112, 210404 (2014).
Nimmrichter, S., Hornberger, K. & Hammerer, K. Optomechanical sensing of spontaneous wave-function collapse. Phys. Rev. Lett. 113, 020405 (2014).
Diósi, L. Testing spontaneous wave-function collapse models on classical mechanical oscillators. Phys. Rev. Lett. 114, 050403 (2015).
Vinante, A. et al. Upper bounds on spontaneous wave-function collapse models using millikelvin-cooled nanocantilevers. Phys. Rev. Lett. 116, 090402 (2016).
Vinante, A., Mezzena, R., Falferi, P., Carlesso, M. & Bassi, A. Improved noninterferometric test of collapse models using ultracold cantilevers. Phys. Rev. Lett. 119, 110401 (2017).
Vinante, A. et al. Narrowing the parameter space of collapse models with ultracold layered force sensors. Phys. Rev. Lett. 125, 100404 (2020).
Ferialdi, L. & Bassi, A. Continuous spontaneous localization reduction rate for rigid bodies. Phys. Rev. A 102, 042213 (2020).
Abbott, B. P. et al. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016).
Vinante, A., The AURIGA Collaboration, et al. Present performance and future upgrades of the auriga capacitive readout. Class. Quantum Grav. 23, S103–S110 (2006).
Armano, M. et al. Sub-femto-g free fall for space-based gravitational wave observatories: LISA Pathfinder results. Phys. Rev. Lett. 116, 231101 (2016).
Armano, M. et al. Beyond the required LISA free-fall performance: new LISA Pathfinder results down to 20 μHz. Phys. Rev. Lett. 120, 061101 (2018).
Carlesso, M., Bassi, A., Falferi, P. & Vinante, A. Experimental bounds on collapse models from gravitational wave detectors. Phys. Rev. D 94, 124036 (2016).
Helou, B., Slagmolen, B., McClelland, D. E. & Chen, Y. LISA Pathfinder appreciably constrains collapse models. Phys. Rev. D 95, 084054 (2017).
Carlesso, M., Paternostro, M., Ulbricht, H., Vinante, A. & Bassi, A. Non-interferometric test of the continuous spontaneous localization model based on rotational optomechanics. New J. Phys. 20, 083022 (2018).
Pontin, A., Bullier, N., Toroš, M. & Barker, P. Ultranarrow-linewidth levitated nano-oscillator for testing dissipative wave-function collapse. Phys. Rev. Res. 2, 023349 (2020).
Zheng, D. et al. Room temperature test of the continuous spontaneous localization model using a levitated micro-oscillator. Phys. Rev. Res. 2, 013057 (2020).
Donadi, S. et al. Novel CSL bounds from the noise-induced radiation emission from atoms. Eur. Phys. J. C 81, 773 (2021).
Donadi, S. et al. Underground test of gravity-related wave function collapse. Nat. Phys. 17, 74–78 (2021).
Diósi, L. & Lukács, B. Calculation of X-ray signals from Károlyházy hazy space-time. Phys. Lett. A 181, 366–368 (1993).
Karolyhazy, F. Gravitation and quantum mechanics of macroscopic objects. Il Nuovo Cim. A 42, 390–402 (1966).
Fu, Q. Spontaneous radiation of free electrons in a nonrelativistic collapse model. Phys. Rev. A 56, 1806–1811 (1997).
Tinkham, M. Introduction to Superconductivity (McGraw Hill, 1996).
Leggett, A. J. Macroscopic quantum systems and the quantum theory of measurement. Prog. Theor. Phys. Suppl. 69, 80–100 (1980).
Friedman, J. R., Patel, V., Chen, W., Tolpygo, S. K. & Lukens, J. E. Quantum superposition of distinct macroscopic states. Nature 406, 43–46 (2000).
Rae, A. I. M. Can GRW theory be tested by experiments on SQUIDS? J. Phys. A 23, L57–L60 (1989).
Buffa, M., Nicrosini, O. & Rimini, A. Dissipation and reduction effects of spontaneous localization on superconducting states. Found. Phys. Lett. 8, 105–125 (1995).
Crowe, J. W. Trapped-flux superconducting memory. IBM J. Res. Dev. 1, 294–303 (1957).
Lochan, K., Das, S. & Bassi, A. Constraining continuous spontaneous localization strength parameter λ from standard cosmology and spectral distortions of cosmic microwave background radiation. Phys. Rev. D 86, 065016 (2012).
Adler, S. L., Bassi, A., Carlesso, M. & Vinante, A. Testing continuous spontaneous localization with Fermi liquids. Phys. Rev. D 99, 103001 (2019).
Tilloy, A. & Stace, T. M. Neutron star heating constraints on wave-function collapse models. Phys. Rev. Lett. 123, 080402 (2019).
Josset, T., Perez, A. & Sudarsky, D. Dark energy from violation of energy conservation. Phys. Rev. Lett. 118, 021102 (2017).
Perez, A., Sahlmann, H. & Sudarsky, D. On the quantum origin of the seeds of cosmic structure. Class. Quantum Grav. 23, 2317–2354 (2006).
Landau, S. J., Scóccola, C. G. & Sudarsky, D. Cosmological constraints on nonstandard inflationary quantum collapse models. Phys. Rev. D 85, 123001 (2012).
Das, S., Lochan, K., Sahu, S. & Singh, T. P. Quantum to classical transition of inflationary perturbations: continuous spontaneous localization as a possible mechanism. Phys. Rev. D 88, 085020 (2013).
Cañate, P., Pearle, P. & Sudarsky, D. Continuous spontaneous localization wave function collapse model as a mechanism for the emergence of cosmological asymmetries in inflation. Phys. Rev. D 87, 104024 (2013).
Das, S., Sahu, S., Banerjee, S. & Singh, T. P. Classicalization of inflationary perturbations by collapse models in light of BICEP2. Phys. Rev. D 90, 043503 (2014).
León, G., Landau, S. J. & Piccirilli, M. P. Inflation including collapse of the wave function: the quasi-de Sitter case. Eur. Phys. J. C 75, 393 (2015).
Banerjee, S., Das, S., Kumar, K. S. & Singh, T. P. Signatures of spontaneous collapse-dynamics-modified single-field inflation. Phys. Rev. D 95, 103518 (2017).
León, G. & Piccirilli, M. P. Generation of inflationary perturbations in the continuous spontaneous localization model: the second order power spectrum. Phys. Rev. D 102, 043515 (2020).
Martin, J. & Vennin, V. Cosmic microwave background constraints cast a shadow on continuous spontaneous localization models. Phys. Rev. Lett. 124, 080402 (2020).
Gundhi, A., Gaona-Reyes, J. L., Carlesso, M. & Bassi, A. Impact of dynamical collapse models on inflationary cosmology. Phys. Rev. Lett. 127, 091302 (2021).
Bengochea, G. R., León, G., Pearle, P. & Sudarsky, D. Discussions about the landscape of possibilities for treatments of cosmic inflation involving continuous spontaneous localization models. Eur. Phys. J. C 80, 1021 (2020).
Goldwater, D., Paternostro, M. & Barker, P. Testing wave-function-collapse models using parametric heating of a trapped nanosphere. Phys. Rev. A 94, 010104 (2016).
Schrinski, B., Stickler, B. A. & Hornberger, K. Collapse-induced orientational localization of rigid rotors. J. Opt. Soc. Am. B 34, C1–C7 (2017).
Gierse, A. et al. A fast and self-acting release-caging-mechanism for actively driven drop tower systems. Microgravity Sci. Technol. 29, 403–414 (2017).
Lotz, C. et al. Tests of additive manufacturing and other processes under space gravity conditions in the Einstein-Elevator. Logistics Journal: Proceedings 2020 (2020).
Kaltenbaek, R. et al. Macroscopic quantum resonators (MAQRO): 2015 update. EPJ Quantum Technol. 3, 5 (2016).
Elliott, E. R., Krutzik, M. C., Williams, J. R., Thompson, R. J. & Aveline, D. C. NASA’s Cold Atom Lab (CAL): system development and ground test status. npj Microgravity 4, 16 (2018).
Paris, M. G. A. Quantum estimation for quantum technology. Int. J. Quantum Technol. 7, 125–137 (2009).
Brunelli, M., Olivares, S. & Paris, M. G. A. Qubit thermometry for micromechanical resonators. Phys. Rev. A 84, 032105 (2011).
Brunelli, M., Olivares, S., Paternostro, M. & Paris, M. G. A. Qubit-assisted thermometry of a quantum harmonic oscillator. Phys. Rev. A 86, 012125 (2012).
Schrinski, B., Nimmrichter, S. & Hornberger, K. Quantum-classical hypothesis tests in macroscopic matter-wave interferometry. Phys. Rev. Res. 2, 033034 (2020).
Schrinski, B., Hornberger, K. & Nimmrichter, S. How to rule out collapse models with BEC interferometry. Preprint at https://arxiv.org/abs/2008.13580 (2020).
Marchese, M. M., Belenchia, A., Pirandola, S. & Paternostro, M. An optomechanical platform for quantum hypothesis testing for collapse models. New J. Phys. 23, 043022 (2021).
Adler, S. L. & Bassi, A. Collapse models with non-white noises. J. Phys. A 40, 15083 (2007).
Smirne, A. & Bassi, A. Dissipative continuous spontaneous localization (CSL) model. Sci. Rep. 5, 12518 (2015).
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).
Nobakht, J., Carlesso, M., Donadi, S., Paternostro, M. & Bassi, A. Unitary unraveling for the dissipative continuous spontaneous localization model: application to optomechanical experiments. Phys. Rev. A 98, 042109 (2018).
Carlesso, M., Ferialdi, L. & Bassi, A. Colored collapse models from the non-interferometric perspective. Eur. Phys. J. D 72, 159 (2018).
Vinante, A., Gasbarri, G., Timberlake, C., Toroš, M. & Ulbricht, H. Testing dissipative collapse models with a levitated micromagnet. Phys. Rev. Res. 2, 043229 (2020).
Toroš, M., Gasbarri, G. & Bassi, A. Colored and dissipative continuous spontaneous localization model and bounds from matter-wave interferometry. Phys. Lett. A 381, 3921–3927 (2017).
We acknowledge fruitful discussions with R. Penrose and A. Vinante on various aspects of the models and related experiments. M.C. and M.P. are supported by UK EPSRC (grant no. EP/T028106/1). S.D. and A.B. acknowledge financial support from INFN. L.F., M.P., H.U. and A.B. acknowledge financial support from the H2020 FET Project TEQ (grant no. 766900). M.P. acknowledges the SFI-DfE Investigators Programme (grant no. 15/IA/2864), the Leverhulme Trust Research Project Grant UltraQute (grant no. RGP-2018-266), the Royal Society Wolfson Research Fellowship scheme (grant no. RSWF\R3\183013) and International Mobility Programme. H.U. acknowledges financial support from the Leverhulme Trust (grant no. RPG-2016-04) and EPSRC (grant no. EP/V000624/1). A.B. acknowledges the Foundational Questions Institute and Fetzer Franklin Fund, a donor advised fund of Silicon Valley Community Foundation (grant no. FQXi-RFP-CPW-2002), and the University of Trieste.
The authors declare no competing interests.
Peer review information
Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Carlesso, M., Donadi, S., Ferialdi, L. et al. Present status and future challenges of non-interferometric tests of collapse models. Nat. Phys. 18, 243–250 (2022). https://doi.org/10.1038/s41567-021-01489-5
This article is cited by
Nature Physics (2022)