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Testing variants of the Diósi–Penrose collapse model with public XENONnT data, and heating predictions of a parameter-free model with a phonon-scale cutoff

Jeongbin Im

Published Oct 10, 2026• 0 citations
Publisher

Abstract

Predictions of the Diósi–Penrose (DP) gravity-related collapse model depend strongly on the mass-density smoothing length R₀ and on the frequency spectrum of the gravitational fluctuations. We reanalyze the public low-energy electronic-recoil data of XENONnT (1–30 keV, 433 events, 1.16 t·yr) with an unbinned likelihood and report four results. First, when R₀ exceeds the atomic size, the equivalence principle makes the nucleus and its electrons accelerate together, and low-energy X-ray emission is strongly cancelled (about 2×10⁻⁴ at 1 keV and 0.16 at 10 keV for xenon). Including this screening, the bound on the white-noise DP model is R₀ > ~0.9 nm, much weaker than the unscreened value (~4.0 nm). Second, the reported bound R₀ > 2.8 nm of an earlier collapse analysis of XENONnT data appears to differ from the Majorana analysis in signal normalization by a factor π^(3/2). With the same normalization it corresponds to 1.56 nm, in agreement with the 1.52 nm we obtain under the same conditions. Third, an 'atomic-unit' variant, with R₀ set to the atomic radius and the fluctuation cutoff set to the electronic time scale, cannot be decided with these data: its verdict ranges from allowed (prediction/limit 0.006) to excluded (11) depending on how strongly the electrons co-move with the nucleus. Fourth, a parameter-free 'phonon-unit' variant, with both R₀ and the cutoff fixed by the lattice vibration of the same nucleus (Debye–Waller rms displacement and Debye frequency), passes the X-ray data independently of the screening treatment and predicts spontaneous heating of about 9.4 pW/kg in copper at cryogenic temperature. This lies just below the currently known unexplained heat-leak limit (~10 pW/kg). X-rays cannot separate the two variants; the (atomic mass × Debye temperature)^(3/2) heating scaling predicted by the phonon-unit variant can be tested by comparing heat leaks in tungsten and aluminium (a factor of about 16).“v2: removed comparison with a withdrawn preprint; added comparison with the XENON collaboration analysis (arXiv:2506.05507) and the 8π convention conversion.”

DOI
10.5281/zenodo.23272334

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arXiv:2506.05507•Physical Review Letters•Jan 22, 2026•2 citations
Predictions of the Diósi–Penrose (DP) gravity-related collapse model depend strongly on the mass-density smoothing length R₀ and on the frequency spectrum of the gravitational fluctuations. We reanalyze the public low-energy electronic-recoil data of XENONnT (1–30 keV, 433 events, 1.16 t·yr) with an unbinned likelihood and report four results. First, when R₀ exceeds the atomic size, the equivalence principle makes the nucleus and its electrons accelerate together, and low-energy X-ray emission is strongly cancelled (about 2×10⁻⁴ at 1 keV and 0.16 at 10 keV for xenon). Including this screening, the bound on the white-noise DP model is R₀ > ~0.9 nm, much weaker than the unscreened value (~4.0 nm). Second, the reported bound R₀ > 2.8 nm of an earlier collapse analysis of XENONnT data appears to differ from the Majorana analysis in signal normalization by a factor π^(3/2). With the same normalization it corresponds to 1.56 nm, in agreement with the 1.52 nm we obtain under the same conditions. Third, an 'atomic-unit' variant, with R₀ set to the atomic radius and the fluctuation cutoff set to the electronic time scale, cannot be decided with these data: its verdict ranges from allowed (prediction/limit 0.006) to excluded (11) depending on how strongly the electrons co-move with the nucleus. Fourth, a parameter-free 'phonon-unit' variant, with both R₀ and the cutoff fixed by the lattice vibration of the same nucleus (Debye–Waller rms displacement and Debye frequency), passes the X-ray data independently of the screening treatment and predicts spontaneous heating of about 9.4 pW/kg in copper at cryogenic temperature. This lies just below the currently known unexplained heat-leak limit (~10 pW/kg). X-rays cannot separate the two variants; the (atomic mass × Debye temperature)^(3/2) heating scaling predicted by the phonon-unit variant can be tested by comparing heat leaks in tungsten and aluminium (a factor of about 16).“v2: removed comparison with a withdrawn preprint; added comparison with the XENON collaboration analysis (arXiv:2506.05507) and the 8π convention conversion.”
In the Diósi–Penrose (DP) model a superposition of two mass distributions decays at the rate E_G/ħ. Diósi's master equation uses the mass-density operator smeared over a length R0; Penrose's formulation uses the density of the stationary state, and the "parameter-free" choice R0 = u_rms (the zero-point amplitude) links the two. This preprint examines what each choice implies for spontaneous heating and for collapse rates, and states separately which results are standard and which are new. Main results:• Heating per unit mass is 2πGħ∫g², i.e. Għ/(4√π σxσyσz) for Gaussian smearing of per-axis widths σi. With R0 equal to the per-axis zero-point amplitude, Diósi's functional reproduces Penrose's E_G for displacements smaller than the lattice spacing.• For a crystal ball, E_G splits exactly into a continuum term and a per-atom granular term. The continuum term is already contained in the per-atom term (the gravitational analogue of the Lorentz local field), the granular term is lattice periodic, and it carries a Madelung reduction of 0.90 (Cu) and 0.29 (⁴He).• Copper is predicted to heat at 12.1–12.8 pW/kg. This is in mild tension with the 10 pW/kg figure adopted after background subtraction from the Bayreuth heat leak.• The published Debye–Waller values of hcp ⁴He follow a convention in which the reported ⟨u²⟩ is half the one-dimensional mean-square displacement. One direct cross-check and four consistency checks support this reading. With it, the solid-helium prediction becomes 6–8 fW/kg instead of 21 fW/kg.• For any liquid (⁴He or ³He) the one-body density is uniform, so Penrose's granular E_G vanishes. The solid/liquid ⁴He collapse-rate ratio is ≈6 for d ≪ u, 2.8 at 0.2 nm and 1.15 at 1 nm, which quantifies a conjecture of Diósi (2013).• Heating under Penrose's prescription depends on the dynamical completion. For every completion that splits ⟨ρ⟩ into non-negative pieces, the liquid heats at most 2πGħn = 1.15 fW/kg; maximal localization then gives a liquid/solid ratio of 0.155. Density-matrix and configuration-based completions give anything from ~10⁻²⁶ to order one.• Experiment: – Ionizing radiation deposits nearly the same power per kilogram in every material and therefore mimics the fixed-R0 signal. – Underground at LNGS, unshielded environmental gammas still deposit 0.6–8 pW/kg, so ≥20 cm of lead is needed. – The nearest-term test of the zero-point prescription is to compare the heat leaks of heavy, stiff metals with copper; tungsten is predicted at ≈77 pW/kg, six times copper. – Underground helium calorimetry at 1–0.1 pW/kg would test colored fixed-R0 models up to R0 ≈ 10–21 pm, provided the cell-wall heat release can be subtracted to 5–0.5%.
VERSION NOTE (v2, 2026-07-02): This version supersedes v1 (April 2026). The central empirical-viability claims of v1 — a thermodynamically viable collapse kernel and a favorable DESI DR1 cosmological signature — were falsified by the author's own subsequent analysis. Fixing the smearing length to its holographically mandated value forces confrontation with the full hierarchy of collapse bounds, where spontaneous-heating measurements exclude it by ~9 orders of magnitude. The work has been rewritten as a parameter-free no-go constraint. v1 is retained below for the version record but should not be cited as a viability result. ABSTRACT (v2): The Diósi–Penrose (DP) model of gravity-induced wavefunction collapse requires an ad hoc mass-smearing length, set phenomenologically at the nucleon scale, R0 ~ 1e-15 m. We show that this scale is fixed by holographic cosmological geometry: evaluating the Károlyházy metric variance over the cosmological apparent horizon, as mandated by the Bousso covariant entropy bound, yields R0 = (lP^2 RH)^(1/3) = 3.3 fm from measured constants alone — a parameter-free reproduction of the historical choice. The decoherence-time kinematics survive every current test: a quantum–classical partition at m_crit ≈ 120 m_e protects atomic chemistry (electron tau ~ 1e21 s) and matter-wave interferometry (C60: ~115 yr) while imposing definiteness on macroscopic bodies, with the ambiguous mesoscopic window falling in the macromolecular regime accessible to near-term interferometry. The standard dynamical realization does not survive. The Einstein Equivalence Principle suppresses single-nucleus dipole bremsstrahlung by a derived factor (k_X R0)^2 ≈ 3e-8, and any noise cutoff below 1e18 Hz evades the underground X-ray bound; but neither defense touches spontaneous heating, which with the standard prefactor predicts ~28 mW/kg — nine orders of magnitude above cryogenic heat-leak ceilings. The heating is charge-independent and probes THz phonons via the relative momentum diffusion of atoms separated by 1e5 correlation lengths, so it is immune to the equivalence principle and robust to any high-frequency cutoff. The framework derives exactly two temporal scales (the pixel light-crossing rate ~1e22 Hz and the horizon refresh rate ~1e-19 Hz); neither lands in the fifteen-decade escape window, and inserting one by hand reinjects the free parameter the construction eliminates. We conclude that if objective collapse is sourced by cosmological holographic geometry, it cannot be mediated by continuous stochastic momentum diffusion: a parameter-free no-go constraint forcing gravity-induced reduction toward non-dissipative or purely kinematic mechanisms.
In 2021, a low-background experiment at the Gran Sasso National Laboratory searched for spontaneous radiation predicted by the standard Markovian Diósi-Penrose (DP) dynamics and obtained the new bound R0>5.4×10−11 mR_0 > 5.4 \times 10^{-11}\,\mathrm{m}R0​>5.4×10−11m at 95%95\%95% probability for the short-length cutoff parameter. For germanium at the experimental temperature, the parameter-free prescription identifying R0R_0R0​ with the spatial quantum spread of a nucleus gives R0≃5×10−12 mR_0 \simeq 5 \times 10^{-12}\,\mathrm{m}R0​≃5×10−12m. That particular combination, Diósi's stochastic dynamics and the Penrose-motivated mass-density resolution, was therefore excluded. Subsequent searches strengthened the cutoff bound. The Majorana Demonstrator improved it in 2022, and XENONnT has now obtained the world-leading limits R0>4.9×10−10 mR_0 > 4.9 \times 10^{-10}\,\mathrm{m}R0​>4.9×10−10m at 90%90\%90% confidence level and R0>4.5×10−10 mR_0 > 4.5 \times 10^{-10}\,\mathrm{m}R0​>4.5×10−10m at 95%95\%95% confidence level. These advances reinforce the 2021 exclusion but do not alter its logical scope: they \emph{parametrically constrain} the Markovian, effectively white-noise DP dynamics, not Penrose's (and Diósi's) lifetime criterion independently of a dynamics, and not all colored-noise, dissipative, or otherwise modified gravity-related spontaneous collapse theories. We reconstruct what Gran Sasso did and did not rule out and place that conclusion in the present experimental context.
The possibility that the collapse of the wave function in quantum mechanics is real and ultimately connected to (classical) gravity has been debated for decades with main contributions by Diósi and Penrose (DP). In particular, Diósi proposed a noise-based dynamical reduction model, which captures the same order of magnitudes for the collapse time suggested by Penrose based on heuristic arguments. This is known in the literature as the DP model (Diósi–Penrose). A peculiarity of the DP model is the prediction of spontaneous heating of matter, which can be tested without the need for massive quantum superpositions. Notably, a very similar effect is predicted by recent theoretical approaches to gravity as a classical-only information channel. Here, we reconsider the current constraints on the DP model from spontaneous heating by analyzing experimental situations not properly considered before. We argue that the parameter-free version of the DP model is close to be ruled out by standard heat leak measurements at ultralow temperatures with a conclusive exclusion likely within reach with existing technology. This result would strengthen a recent claim of exclusion inferred by spontaneous x-ray emission experiments, which relies on the somewhat stronger assumption that the DP noise field is white up to x-ray frequencies.
We report on the search for x-ray radiation as predicted from dynamical quantum collapse with low-energy electronic recoil data in the energy range of 1–140 keV from the first science run of the XENONnT dark matter detector. Spontaneous radiation is an unavoidable effect of dynamical collapse models, which were introduced as a possible solution to the long-standing measurement problem in quantum mechanics. The analysis utilizes a model that for the first time accounts for cancellation effects in the emitted spectrum, which arise in the x-ray range due to the opposing electron-proton charges in xenon atoms. New world-leading limits on the free parameters of the Markovian continuous spontaneous localization and Diósi-Penrose models are set, improving previous best constraints by two orders of magnitude and a factor of five, respectively. For the strength and correlation length of the continuous spontaneous localization model, values in the originally proposed parameter ranges are experimentally excluded for the first time.
We report on the search for x-ray radiation as predicted from dynamical quantum collapse with low-energy electronic recoil data in the energy range of 1-140 keV from the first science run of the XENONnT dark matter detector. Spontaneous radiation is an unavoidable effect of dynamical collapse models, which were introduced as a possible solution to the long-standing measurement problem in quantum mechanics. The analysis utilizes a model that for the first time accounts for cancellation effects in the emitted spectrum, which arise in the x-ray range due to the opposing electron-proton charges in xenon atoms. New world-leading limits on the free parameters of the Markovian continuous spontaneous localization and Diósi-Penrose models are set, improving previous best constraints by two orders of magnitude and a factor of five, respectively. For the strength and correlation length of the continuous spontaneous localization model, values in the originally proposed parameter ranges are experimentally excluded for the first time.