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arXiv:2601.00651

Experimental exclusion of a generalized Károlyházy gravity-induced decoherence model

Nicola Bortolotti, Kristian Piscicchia, Matthias Laubenstein, Simone Manti, Antonino Marcianò, Federico Nola, Catalina Curceanu

quant-phSubmitted Jan 2, 2026• Announced Jan 5, 2026• 0 citations
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Abstract

We report new experimental constraints on the generalized version of the gravity-induced decoherence model originally proposed by Károlyházy. Using data collected by the VIP Collaboration at the INFN Gran Sasso National Laboratory with a high-purity germanium detector, we derive an improved lower bound on the spatial correlation length $R_K$ characterizing metric fluctuations in the model. We obtain a bound $R_K > 4.64$ m (95\% C.L.), which exceeds by more than an order of magnitude the previous experimental limit. When combined with the theoretical upper bound $R_K <1.98$ m derived from macroscopic localization requirements, our result excludes the generalized Károlyházy model. The same conclusion applies to an associated non-Markovian formulation of the Continuous Spontaneous Localization (CSL) model. Our findings significantly tighten experimental constraints on gravity-related decoherence scenarios and demonstrate the sensitivity of underground low-background experiments to foundational modifications of quantum mechanics.

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10 pages, 4 figures

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We report new experimental constraints on the generalized version of the gravity-induced decoherence model originally proposed by Károlyházy. Using data collected by the VIP Collaboration at the INFN Gran Sasso National Laboratory with a high-purity germanium detector, we derive an improved lower bound on the spatial correlation length RKR_KRK​ characterizing metric fluctuations in the model. We obtain a bound RK>4.64R_K > 4.64RK​>4.64 m (95% C.L.), which exceeds by more than an order of magnitude the previous experimental limit. When combined with the theoretical upper bound RK<1.98R_K <1.98RK​<1.98 m derived from macroscopic localization requirements, our result excludes the generalized Károlyházy model. The same conclusion applies to an associated non-Markovian formulation of the Continuous Spontaneous Localization (CSL) model. Our findings significantly tighten experimental constraints on gravity-related decoherence scenarios and demonstrate the sensitivity of underground low-background experiments to foundational modifications of quantum mechanics.
Abstract We report new experimental constraints on the generalized version of the gravity-induced decoherence model originally proposed by Károlyházy. Using data collected by the VIP Collaboration at the INFN Gran Sasso National Laboratory with a high-purity germanium detector, we derive an improved lower bound on the spatial correlation length R K characterizing metric fluctuations in the model. We obtain a bound R K > 4.64 m (95% C.L.), which exceeds by more than an order of magnitude the previous experimental limit. When combined with the theoretical upper bound R K < 1.98 m derived from macroscopic localization requirements, our result excludes the generalized Károlyházy model. The same conclusion applies to an associated non-Markovian formulation of the continuous spontaneous localization model. Our findings significantly tighten experimental constraints on gravity-related decoherence scenarios and demonstrate the sensitivity of underground low-background experiments to foundational modifications of quantum mechanics.
The unification of quantum mechanics and general relativity remains one of the central open problems in modern physics. In recent decades, increasing attention has focused on the idea of gravitazing quantum mechanics represents the approach to modify quantum mechanics in order to accommodate for gravity, rather than modifying gravity by quantizing it. Within this perspective, gravity is expected to play a privileged role in resolving the longstanding measurement problem. At the same time, the growing sensitivity of underground experiments searching for the characteristic electromagnetic signature of wave-function collapse – known as spontaneous radiation – has placed stringent constraints on theoretical models. In this work, we present the phenomenological and experimental efforts of the VIP collaboration at the Gran Sasso National Laboratories (INFN), which currently provides some of the most stringent limits on an entire class of spontaneous collapse models.
It has been suggested in the literature that spatial coherence of the wave function can be dynamically suppressed by fluctuations in the spacetime geometry. These fluctuations represent the minimal uncertainty that is present when one probes spacetime geometry with a quantum probe. Two similar models have been proposed, one by Diósi [D-model] and one by Karolyhazy and collaborators [K-model], based on apparently unrelated minimal spacetime bounds. The two models arrive at somewhat different expressions for the dependence of the localization coherence length on the mass and size of the quantum object. In the present article we compare and contrast the two models from three aspects: (i) comparison of the spacetime bounds, (ii) method of calculating decoherence time, (iii) comparison of noise correlation. We show that under certain conditions the minimal spacetime bounds in the two models can be derived one from the other. We argue that the methods of calculating the decoherence time are equivalent. We re-derive the two-point correlation for the fluctuation potential in the K-model, and confirm the earlier result of Diósi and Lukács that it is non-white noise, unlike in the D-model, where the corresponding correlation is white noise in time. This seems to be the origin of the different results in the two models. We derive the non-Markovian master equation for the K-model. We argue that the minimal spacetime bound cannot predict the noise correlation uniquely, and additional criteria are necessary to accurately determine the effects of gravitationally induced decoherence.
Quantum mechanics is a cornerstone of modern physics and at the very basis of the Standard Model. However, decades-old open questions at its foundations, such as the "measurement problem" and the wave function collapse are still with us. Moreover, theories beyond the Standard Model often include extra-dimensions and violation of the Lorentz/Poincaré symmetries which could entail a departure from the predictions of the standard quantum mechanics. At the Gran Sasso underground laboratory in Italy, we search for small, beyond the quantum theory signals using radiation detectors. In particular, emission of spontaneous radiation is predicted by gravity- related and continuous spontaneous localization (CSL) collapse models. We have ruled out the natural parameter-free version of the Diósi-Penrose (DP) model, and put stringent limits on the CSL model. In addition, with the VIP-2 experiment we are searching for possible violations of the Pauli Exclusion Principle (PEP) in forbidden atomic transitions. The impact of this research on quantum gravity models, as well as its experimental upgrade VIP-3 is also discussed.
It has already been suggested that quantum theory needs to be reformulated or modified in order to explain the measurement process and the successive collapse of the wave- function. However, there are also models of another type which keep quantum theory intact and instead modify the classical gravity by introducing stochasticity to it. These models suggest that there is a fluctuation in the background gravitational field which eventually results in the decoherence of the wavefunction. These fluctuations limit the precision with which one can measure the properties of a spacetime geometry with a quantum probe. Two similar models along this line have been suggested by Karolyhazy (K-model) and Diósi(D-model). They are based upon apparently different spacetime bounds. The results obtained for the coherence length are also somewhat different. In this article, we show that, given certain conditions apply, the minimal spacetime bounds in these two models are equivalent. We also derive the two-point correlation for the fluctuation potential in K-model which turns out to be non-white, unlike in D-model, where the corresponding correlation is white noise in time. In our opinion, this is the origin of discrepancy in the predictions of the two models. We argue that the noise correlation cannot be determined uniquely from a given spacetime bound.
Several phenomenological approaches to quantum gravity predict the existence of a minimal measurable length and/or a maximum measurable momentum near the Planck scale. When embedded into the framework of quantum mechanics, such constraints induce a modification of the canonical commutation relations and thus a generalization of the Heisenberg uncertainty relations, commonly referred to as generalized uncertainty principle (GUP). Different models of quantum gravity imply different forms of the GUP. For instance, in the framework of string theory the GUP is quadratic in the momentum operator, while in the context of doubly special relativity it includes an additional linear dependence. Among the possible physical consequences, it was recently shown that the quadratic GUP induces a universal decoherence mechanism, provided one assumes a foamy structure of quantum spacetime close to the Planck length. Along this line, in the present work we investigate the gravitational decoherence associated to the linear-quadratic GUP and we compare it with the one associated to the quadratic GUP. We find that, despite their similarities, the two generalizations of the Heisenberg uncertainty principle yield decoherence times that are completely uncorrelated and significantly distinct. Motivated by this result, we introduce a theoretical and experimental scheme based on cavity optomechanics to measure the different time evolution of nonlocal quantum correlations corresponding to the two aforementioned decoherence mechanisms. We find that the deviation between the two predictions occurs on time scales that are macroscopic and thus potentially amenable to experimental verification. This scenario provides a possible setting to discriminate between different forms of the GUP and therefore different models of quantum gravity.