⚛️ quantum physics

Did the Gran Sasso Experiment Rule Out the Diósi-Penrose Theory? Musing on the 2021 Result and the Present Experimental Status

This paper clarifies that while recent experiments, including the 2021 Gran Sasso result and subsequent limits from Majorana and XENONnT, have parametrically ruled out the specific combination of Markovian Diósi-Penrose dynamics with a particular mass-density resolution, they have not excluded the broader Penrose lifetime criterion or other modified gravity collapse theories.

Original authors: Catalina Curceanu, Nicola Bortolotti, Lajos Diósi, Simone Manti, Kristian Piscicchia

Published 2026-10-27

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CC BY 4.0

Original authors: Catalina Curceanu, Nicola Bortolotti, Lajos Diósi, Simone Manti, Kristian Piscicchia

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep within the quiet rock of the Italian Apennines, far beneath the noise of the surface world, scientists have long listened for a whisper that might change our understanding of reality. This whisper concerns a fundamental question: why do the strange, fuzzy rules of the quantum world, which govern atoms and light, give way to the solid, predictable rules of everyday life? For decades, a leading idea suggested that gravity itself might be the force that forces the quantum world to "choose" a single state, collapsing the fuzzy possibilities into the definite reality we see. This concept, known as the Diósi-Penrose theory, proposes that when an object becomes large enough, its own gravitational pull makes it impossible for it to exist in two places at once. If this theory is correct, the process of this collapse should not be silent; it should produce a faint, spontaneous radiation, a tiny burst of energy released as the universe settles a quantum superposition. Detecting this radiation would be a monumental discovery, proving that gravity plays a direct role in the collapse of the wave function. However, if the radiation is absent, it means the theory, in its simplest form, does not describe nature.

In 2021, a team of researchers at the Gran Sasso National Laboratory set out to find this radiation. They placed a high-purity germanium detector deep underground, shielding it from cosmic rays and other background noise to create the quietest possible listening post. Their goal was to catch the specific signal predicted by the standard version of the Diósi-Penrose model. This model relies on a specific set of assumptions: that the collapse happens randomly and continuously, like a steady stream of white noise, and that the "resolution" of the mass involved—the smallest distance at which the theory can distinguish between two points—is determined by the natural, quantum jitter of the atomic nuclei inside the detector. If this specific combination of ideas were true, the detector should have seen a clear excess of radiation. Instead, the experiment found nothing. The data showed no sign of the predicted signal, leading the researchers to conclude that this particular, parameter-free version of the theory is incorrect. The natural, unadjusted prediction for how the theory should work with germanium was ruled out by a wide margin.

The story did not end there. In the years following the Gran Sasso result, other experiments joined the search, each bringing more sensitive equipment and larger amounts of material to the task. The Majorana Demonstrator, using enriched germanium, and later the XENONnT dark matter detector, using liquid xenon, repeated the search with even greater precision. These newer experiments confirmed the earlier findings and pushed the boundaries even further. They established that if this type of gravity-induced collapse exists, the "resolution" parameter must be much larger than the natural size of the atomic nuclei. Specifically, the XENONnT experiment set a new limit, showing that the cutoff must be larger than 4.5 × 10⁻¹⁰ meters at a 95 percent confidence level. This means the theory, in its standard form, is constrained to a much narrower range of possibilities than previously thought. The experiments have effectively closed the door on the idea that the collapse happens exactly as the simplest version of the theory predicted, where the resolution is just the natural spread of the nuclei.

However, the authors of this paper are careful to clarify exactly what has been ruled out and what remains possible. They emphasize that the experiments did not disprove the entire concept of gravity-related collapse, nor did they disprove the general idea that gravity causes the wave function to collapse. What was rejected was a specific, elegant package: the combination of a standard, random noise model with a specific, natural way of measuring the size of the mass. The theory could still be correct if the "noise" driving the collapse is different—perhaps it is not a steady white noise but a more complex, colored noise that changes over time, or if the resolution of the mass is not determined by the natural jitter of the nuclei but by some other, larger scale. The experiments have not found a universal "no" to gravity's role in collapse; rather, they have provided a very precise "no" to one specific way of writing the rules.

This distinction is vital for the future of the field. The scientific community now knows that the simplest, most natural version of the Diósi-Penrose model does not match reality. The path forward requires theorists to refine their ideas, perhaps by adjusting how the noise behaves or by rethinking how the mass is resolved at tiny distances. The experiments have not solved the mystery of why the quantum world becomes the classical world, but they have removed a major candidate for the solution. By narrowing the space of viable theories, these deep underground searches have forced a more precise conversation. The silence of the detectors is not a failure; it is a clear message that nature is more complex than the simplest equations suggested, guiding scientists toward a more accurate understanding of the fundamental forces that shape our reality.

Technical Summary: Did the Gran Sasso Experiment Rule Out the Diósi-Penrose Theory?

Problem and Context
The paper addresses a persistent ambiguity in the interpretation of experimental tests regarding gravity-related spontaneous wave-function collapse. Specifically, it clarifies the logical scope of the 2021 Gran Sasso experiment and subsequent searches (Majorana Demonstrator, XENONnT) concerning the Diósi-Penrose (DP) model. The authors note that while the 2021 result was sometimes summarized as "ruling out the DP model," this conflation is technically inaccurate. The "DP model" comprises distinct, logically separable ingredients: a gravitational estimate for collapse time, a specific stochastic dynamical equation (Diósi's), a prescription for mass-density resolution (Penrose's), and assumptions about the noise spectrum (Markovian/white noise). The paper argues that experiments constrain specific combinations of these ingredients, not the entire theoretical framework or Penrose's original lifetime criterion in isolation.

Methodology and Theoretical Framework
The paper does not present new experimental data but reconstructs the theoretical and experimental logic of previous studies to define what was actually tested:

Theoretical Distinction: The authors distinguish between the "narrow sense" DP model (the gravitational collapse time estimate $\tau_{DP} = \hbar/E_{DP}$ ) and the "standard" DP dynamics (Diósi's Markovian stochastic master equation). The latter predicts that the localization noise driving collapse also induces momentum diffusion in charged particles, leading to spontaneous radiation.
Resolution Parameter ( $R_0$ ): The theory requires a finite spatial resolution $R_0$ $R_{0}$ to avoid ultraviolet divergence in gravitational self-energy. Two prescriptions are compared:
- Parameter-free: $R_0$ is identified with the quantum positional spread of nuclei in a material (derived from the Debye-Waller factor).
- Parameter-dependent: $R_0$ is a universal phenomenological cutoff to be bounded by experiment.
Experimental Signal: The Gran Sasso, Majorana, and XENONnT experiments searched for the spontaneous radiation predicted by the standard Markovian DP dynamics. The radiation spectrum scales as $R_0^{-3}$ , making the experiments highly sensitive to the cutoff value. The analysis assumes a white-noise (Markovian) spectrum; colored-noise or non-Markovian modifications would alter the high-frequency emission and are not constrained by the same bounds.

Key Results and Experimental Progression
The paper synthesizes the progression of lower bounds on the spatial cutoff parameter $R_0$ (expressed in the Diósi convention):

Gran Sasso (2021): Using a high-purity germanium detector, the experiment found no excess radiation. It established a lower bound of $R_0 > 5.4 \times 10^{-11}$ m (95% probability). This excluded the "natural parameter-free" version of the model, where $R_0$ is calculated from the nuclear spread in germanium ( $R_P \approx 5 \times 10^{-12}$ m), as the experimental limit is roughly 11 times larger than the theoretical prediction.
Majorana Demonstrator (2022/2023): Using enriched germanium, this experiment provided an independent confirmation, improving the bound to $R_0 > 8.7 \times 10^{-11}$ m (95% C.L.).
XENONnT (2026): Using liquid xenon data, this experiment established the current world-leading limits: $R_0 > 4.9 \times 10^{-10}$ m (90% C.L.) and $R_0 > 4.5 \times 10^{-10}$ m (95% C.L.).

Key Contributions
The primary contribution of this paper is a rigorous conceptual clarification of what these experimental results falsify:

Specific Exclusion: The experiments definitively rule out the combination of Diósi's standard Markovian stochastic dynamics and Penrose's parameter-free prescription for mass-density resolution (where $R_0$ is the nuclear spread).
Non-Exclusion: The paper explicitly states that the following were not ruled out:
- The DP model with a free, adjustable cutoff parameter $R_0$ (values above the current experimental bounds remain viable).
- Penrose's gravitational lifetime criterion ( $\tau_{DP}$ ) in isolation, as it does not inherently predict spontaneous radiation without a specific dynamical completion.
- Non-Markovian, colored-noise, dissipative, or relativistic modifications to the collapse dynamics, which could suppress the high-frequency radiation detected in these experiments.
- The general hypothesis that gravity plays a role in wave-function collapse.

Significance and Conclusion
The authors conclude that the scientific value of the experimental sequence (Gran Sasso to XENONnT) lies in its precision rather than its breadth. The results do not "rule out DP" as a monolithic theory but have substantially narrowed the viable theoretical space. The experiments have successfully falsified a specific, historically important, and "economical" realization of the model (the parameter-free, Markovian version). The paper emphasizes that future theoretical developments must provide quantitative predictions for noise spectra and dynamical completions to be testable, and that the exclusion of one specific realization does not invalidate the broader motivation for gravity-related collapse. The paper serves as a conceptual update to ensure the logical scope of the 2021 result is correctly understood in light of subsequent experimental advances.

Technical Summary: Did the Gran Sasso Experiment Rule Out the Diósi-Penrose Theory?

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