We investigate the Di'osi-Penrose (DP) proposal for connecting the collapse of the wave function to gravity. The DP model needs a free parameter, acting as a cutoff to regularize the dynamics, and the predictions of the model highly depend on the value of this cutoff. The Compton wavelength of a nucleon seems to be the most reasonable cutoff value since it justifies the nonrelativistic approach. However, with this value, the DP model predicts an unrealistically high rate of energy increase. Thus, either one is forced to choose a much larger cutoff, which is not physically justified and totally arbitrary, or one needs to include dissipative effects in order to tame the energy increase. Taking the analogy with dissipative collisional decoherence seriously, we develop a dissipative generalization of the DP model. We show that even with dissipative effects, the DP model contradicts known physical facts, unless either the cutoff is kept artificially large or one limits the applicability of the model to massive systems. We also provide an estimation for the mass range of this applicability.
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.
Abstract The possibility that gravity plays a role in the collapse of the quantum wave function has been considered in the literature, and it is of relevance not only because it would provide a solution to the measurement problem in quantum theory, but also because it would give a new and unexpected twist to the search for a unified theory of quantum and gravitational phenomena, possibly overcoming the current impasse. The Diósi–Penrose model is the most popular incarnation of this idea. It predicts a progressive breakdown of quantum superpositions when the mass of the system increases; as such, it is susceptible to experimental verification. Current experiments set a lower bound R 0 ≳ 4 Å for the free parameter of the model, excluding some versions of it. In this work we search for an upper bound, coming from the request that the collapse is effective enough to guarantee classicality at the macroscopic scale: we find out that not all macroscopic systems collapse effectively. If one relaxes this request, a reasonable (although to some degree arbitrary) bound is found to be: R 0 ≲ 10 6 Å. This will serve to better direct future experiments to further test the model.
The Diosi-Penrose model of quantum-classical boundary postulates gravity-related spontaneous wave function collapse of massive degrees of freedom. The decoherence effects of the collapses are in principle detectable if not masked by the overwhelming environmental decoherence. But the DP (or any other, like GRW, CSL) spontaneous collapses are not detectable themselves, they are merely the redundant formalism of spontaneous decoherence. To let DP collapses become testable physics, recently we extended the DP model and proposed that DP collapses are responsible for the emergence of the Newton gravitational force between massive objects. We identified the collapse rate, possibly of the order of 1/ms, with the rate of emergence of the Newton force. A simple heuristic emergence (delay) time was added to the Newton law of gravity. This non-relativistic delay is in peaceful coexistence with Einstein’s relativistic theory of gravitation, at least no experimental evidence has so far surfaced against it. We derive new predictions of such a ‘lazy’ Newton law that will enable decisive laboratory tests with available technologies. The simple equation of ’lazy’ Newton law deserves theoretical and experimental studies in itself, independently of the underlying quantum foundational considerations.
The Diosi-Penrose model of quantum-classical boundary postulates gravity-related spontaneous wave function collapse of massive degrees of freedom. The decoherence effects of the collapses are in principle detectable if not masked by the overwhelming environmental decoherence. But the DP (or any other, like GRW, CSL) spontaneous collapses are not detectable themselves, they are merely the redundant formalism of spontaneous decoherence. To let DP collapses become testable physics, recently we extended the DP model and proposed that DP collapses are responsible for the emergence of the Newton gravitational force between massive objects. We identified the collapse rate, possibly of the order of 1/ms, with the rate of emergence of the Newton force. A simple heuristic emergence (delay) time was added to the Newton law of gravity. This non-relativistic delay is in peaceful coexistence with Einstein's relativistic theory of gravitation, at least no experimental evidence has so far surfaced against it. We derive new predictions of such a 'lazy' Newton law that will enable decisive laboratory tests with available technologies. The simple equation of 'lazy' Newton law deserves theoretical and experimental studies in itself, independently of the underlying quantum foundational considerations.
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.”
This note presents a conceptual modification to the Diósi–Penrose (DP) objective collapse model. The note conjectures that the timescale of wave function collapse (
τ≈ℏ/EG) is influenced not only by the gravitational self-energy (
EG) but also by the asymmetry in the "dispositional thermodynamic capacities" (
S˙disp) of the superposed branches. The proposed modification introduces a multiplicative correction factor, expressed as
τ−1≈(EG/ℏ)⋅[1+f(ΔS˙disp)], ensuring the effect vanishes when branches are thermodynamically symmetric or when
EG approaches zero. This approach is distinctly framed against the existing dissipative-collapse literature (e.g., dissipative DP and CSL variants), as it relies on a between-branch difference rather than a global dissipative term to modulate the collapse rate. The document outlines two hard constraints for this theoretical framework: Degeneracy: Canonical DP tests inherently lack thermodynamic asymmetry (
ΔS˙disp=0), meaning the correction predicts nothing beyond bare DP unless thermal asymmetries (e.g., thermal gradients or substrate proximity) are deliberately engineered. Magnitude: The correction factor must be heavily suppressed below the raw thermal scale, as naive scaling with thermal energy across a mesoscale object's phonon modes would exceed
EG by many orders of magnitude. Finally, the note addresses current barriers to empirical testing. It acknowledges that the conjecture remains practically unfalsifiable at present because the methods required to engineer
ΔS˙disp=0 are degenerate with ordinary, non-gravitational decoherence effects, and no current experimental configuration isolates the proposed mechanism from these confounds. Keywords: Diósi-Penrose Model, Objective Wave Function Collapse, Quantum Decoherence, Gravitational Self-Energy, Dispositional Thermodynamic Capacity, Quantum Foundations, Spontaneous Collapse, Dissipative Collapse.