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Conceptual Note: Branch-Asymmetry Modulation of the Diósi–Penrose Collapse Rate

Jesper Åberg

Published Aug 16, 2026• 0 citations
Publisher

Abstract

This note presents a conceptual modification to the Diósi–Penrose (DP) objective collapse model. The note conjectures that the timescale of wave function collapse ($\tau \approx \hbar / E_G$) is influenced not only by the gravitational self-energy ($E_G$) but also by the asymmetry in the "dispositional thermodynamic capacities" ($\dot{S}_{disp}$) of the superposed branches. The proposed modification introduces a multiplicative correction factor, expressed as $\tau^{-1} \approx (E_G / \hbar) \cdot [1 + f(\Delta\dot{S}_{disp})]$, ensuring the effect vanishes when branches are thermodynamically symmetric or when $E_G$ 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 ($\Delta\dot{S}_{disp} = 0$), 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 $E_G$ 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 $\Delta\dot{S}_{disp} \neq 0$ 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.

DOI
10.5281/zenodo.21965714

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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\tau \approx \hbar / E_Gτ≈ℏ/EG​) is influenced not only by the gravitational self-energy (EGE_GEG​) but also by the asymmetry in the "dispositional thermodynamic capacities" (S˙disp\dot{S}_{disp}S˙disp​) of the superposed branches. The proposed modification introduces a multiplicative correction factor, expressed as τ−1≈(EG/ℏ)⋅[1+f(ΔS˙disp)]\tau^{-1} \approx (E_G / \hbar) \cdot [1 + f(\Delta\dot{S}_{disp})]τ−1≈(EG​/ℏ)⋅[1+f(ΔS˙disp​)], ensuring the effect vanishes when branches are thermodynamically symmetric or when EGE_GEG​ 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\Delta\dot{S}_{disp} = 0ΔS˙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 EGE_GEG​ 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\Delta\dot{S}_{disp} \neq 0ΔS˙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.
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.
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.
The physical mechanism underlying quantum wave-function collapse remains a centralproblem in foundational physics. Objective collapse theories, notably the Penrose-Diósi(DP) model, propose that macroscopic superposition is destroyed by gravitational self-energy∆EG, predicting that collapse time τD = ℏ/∆EG scales strictly with mass. Recent experimental bounds from underground generalized acceleration experiments (AURIGA, Helouet al. 2017) have severely constrained the DP parameter space. We propose an entirelydistinct, falsifiable mechanism: Topological Representation Collapse. Within the DSM-861framework, wave-function collapse is triggered not by static gravity but by dynamic enstrophy strain exceeding the topological melting threshold Em = 695.74 eV. This establishes afalsifiable experimental demarcation line in the mesoscopic regime. We demonstrate fourspecific signatures: (1) Topology vs. Mass—decoherence depends on vorticity, not mass; (2)The Rotor Anomaly—a driven nanomechanical rotor will decohere faster than DP predictswhen rotational energy approaches 695.74 eV; (3) Protein Folding Dynamics—intrinsicallydisordered proteins generate enstrophy gradients that trigger a hard decoherence cutoff; (4)Rigid Mass Coherence—a perfectly rigid, non-rotating mass maintains coherence longer thanDP allows. All four predictions are falsifiable with next-generation mesoscopic superpositionexperiments.
The physical mechanism underlying quantum wave-function collapse remains a central problem in foundational physics. Objective collapse theories, notably the Penrose-Diósi (DP) model,propose that macroscopic superposition is destroyed by gravitational self-energy (∆EG), predicting that collapse scales strictly with mass.We propose an entirely distinct physical mechanism: Topological Representation Collapse.Within the Deterministic Spectral Manifold (DSM-861) framework, wave-function collapse istriggered not by static gravity, but by dynamic enstrophy strain exceeding a specific topologicalmelting threshold (Em ≈ 695.74 eV). This establishes a falsifiable experimental demarcationline in the mesoscopic regime. We demonstrate that highly strained, rapidly rotating, or topologically complex mesoscopic systems (such as driven nanomechanical rotors or rapidly foldingproteins) will undergo spontaneous decoherence significantly faster than predicted by gravityinduced models, while perfectly rigid macroscopic masses may maintain coherence longer.
We evaluate the macroscopic entanglement-loss implications of gravitational time dilation, first identified by Pikovski et al. (2015). By moving beyond the idealized zero-temperature single-mode approximation to a continuous Debye model in the canonical ensemble, we derive the explicit phononic heat-capacity limits for spontaneous gravitational decoherence. We find that the decoherence rate driven by internal time-dilation variance strongly scales with σ∝T5/2\sigma \propto T^{5/2}σ∝T5/2 at ultra-low experimental temperatures (T≪ΘDT \ll \Theta_DT≪ΘD​), vanishing strictly at absolute zero. Furthermore, we demonstrate mathematically that translational invariance renders proper-time differences between spatially distinct branches of an identical matter distribution identically zero. Thus, contrary to the Diósi-Penrose approach, an isolated mass in a pure superposition cannot undergo solely self-gravitational state-collapse. Decoherence requires either an external gravitational potential gradient or internal structural asymmetry. Lastly, we prove that the topological spectral dimension dsd_sds​ of the macroscopic test mass determines the decoherence rate scaling, creating a new class of ultra-sensitive 'fracton-gravity sensors'.