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Gravitational Collapse of Massive Superpositions from a Finite Distinguishability Budget: A Non-Radiating Objective-Collapse Mechanism

Justin Smith

Published Jul 7, 2026• 0 citations
Publisher

Abstract

We derive an objective-collapse prediction for massive spatial superpositions from a singlepremise — that physical distinguishability is finite and discrete — and show that it evades thespontaneous-radiation bounds that exclude the parameter-free Di´osi–Penrose model. The mechanism is conservative: a superposition of a massive body in two locations is a superposition oftwo gravitational configurations, and when the gravitational self-energy difference ∆E betweenthem reaches the capacity of one distinguishability cell, coherence commits, on the timescaleτ ∼ℏ/∆E. This reproduces the Di´osi–Penrose collapse time, here derived rather than posited,with a regularisation length fixed without tuning as the nucleon Compton wavelength, giving acollapse mass ceiling of order 1012–1014 amu. The prediction is consistent with every matterwave interference experiment performed — at the current record (∼ 105 amu) the predictedcoherence time exceeds the experimental one by ten orders of magnitude — and lies withinreach of next-generation nanoparticle interferometry. Crucially, we derive the collapse masterequation and show that the momentum-diffusion coefficient, which controls spontaneous electromagnetic radiation and by which white-noise collapse models are experimentally excluded,vanishes exactly. The reason is structural: because the distinguishability ledger is discrete,the collapse rate as a function of branch separation is identically zero below a threshold — ahard step, not a smooth rise — so its curvature at zero separation, which sets the momentumdiffusion, is exactly zero. Localised charges therefore radiate nothing, and the undergroundradiation bounds do not apply. The result rests on one stated assumption, strict discreteness ofthe distinguishability count, which is the premise itself; granting it, the evasion of the radiationbounds is a theorem rather than a tuning.

DOI
10.5281/zenodo.21237870

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We derive an objective-collapse prediction for massive spatial superpositions from a singlepremise — that physical distinguishability is finite and discrete — and show that it evades thespontaneous-radiation bounds that exclude the parameter-free Di´osi–Penrose model. The mechanism is conservative: a superposition of a massive body in two locations is a superposition oftwo gravitational configurations, and when the gravitational self-energy difference ∆E betweenthem reaches the capacity of one distinguishability cell, coherence commits, on the timescaleτ ∼ℏ/∆E. This reproduces the Di´osi–Penrose collapse time, here derived rather than posited,with a regularisation length fixed without tuning as the nucleon Compton wavelength, giving acollapse mass ceiling of order 1012–1014 amu. The prediction is consistent with every matterwave interference experiment performed — at the current record (∼ 105 amu) the predictedcoherence time exceeds the experimental one by ten orders of magnitude — and lies withinreach of next-generation nanoparticle interferometry. Crucially, we derive the collapse masterequation and show that the momentum-diffusion coefficient, which controls spontaneous electromagnetic radiation and by which white-noise collapse models are experimentally excluded,vanishes exactly. The reason is structural: because the distinguishability ledger is discrete,the collapse rate as a function of branch separation is identically zero below a threshold — ahard step, not a smooth rise — so its curvature at zero separation, which sets the momentumdiffusion, is exactly zero. Localised charges therefore radiate nothing, and the undergroundradiation bounds do not apply. The result rests on one stated assumption, strict discreteness ofthe distinguishability count, which is the premise itself; granting it, the evasion of the radiationbounds is a theorem rather than a tuning.
Version 2.8 — submission manuscript. Preprint prepared for submission to Foundations of Physics. Supersedes v2.6, v2.5, v2.3, v2.2 and v1. A gravitational collapse model in which spacetime geometry is postulated to be irreducibly classical and superpositions of massive systems decay under a stochastic dynamics driven by a physical temporal medium: one stationary noise field combining the Diósi–Penrose spatial kernel with a coloured temporal kernel of finite universal bandwidth ω_u — the single new parameter of the primary model. The decoherence envelope is derived exactly (Gaussian onset, DP exponential tail), and two universality propositions are proved: the DP tail is fixed by the kernel's zero-frequency weight alone, and a Gaussian onset is generic for any finite-bandwidth medium — making the crossover, not any particular kernel, the experimental signature. A selectivity theorem shows each configuration draws its collapse dominantly from noise modes near its own gravitational frequency ΔE_g/ℏ. The parameter-free tuning of earlier versions is retained as named Conjecture C1, with a proof that no single stationary spectrum realises it for all configurations at once. The coloured kernel suppresses collapse-induced spontaneous radiation, reconciling the model with underground null results; heating bounds survive at full strength. Predictions include a closed-form optimal measurement window (separation 0.330 at t = 0.837 τ_dec under C1) and a mass-and-time ceiling on Bell violations, with five falsification conditions. The BMV/GIE treatment is current with the 2024–2026 literature. Changes in v2.8 (Appendix B, B11–B13): universal-bandwidth primary model with derived (ω_u, R_0) window; C1 demoted to conjecture with proved obstruction; no-signalling corrected and branch-conditioned; non-Markovian trajectory literature engaged, Born-rule theorem declared open; one prediction and the "present moment" identification withdrawn with reasons; GIE dispute disentangled; references verified. This paper builds on v1 of the companion collapse-model work (10.5281/zenodo.19960071). The lowest-energy principle assumed here was withdrawn in v2.2 of that paper and does not appear in the current version (v2.8); the framework presented here has not been revised accordingly. Retained as a record of the earlier line of enquiry All revisions, withdrawn claims, and corrected errors are documented in Appendix B; open problems in Section 8. AI tools (Claude, Anthropic) assisted with formalisation and editing; the conceptual framework originated with the author, who takes full responsibility. Full declaration in the manuscript.
We develop a gravitational collapse model in which spacetime geometry is postulated to beirreducibly classical and quantum superpositions of massive systems decay under a stochasticdynamics driven by a physical temporal medium. The model combines the Diósi–Penrosespatial kernel with a coloured temporal kernel of finite correlation time _c; the hypothesis _c τ τ= / E_g renders it parameter-free. The decoherence envelope is derived exactly: Gaussian at ℏ Δearly times, crossing to exponential Diósi–Penrose decay — a signature distinguishing themodel from thermal decoherence and from all Markovian collapse models. The coloured kernelsuppresses collapse-induced spontaneous radiation by ( _c) ², reconciling gravitational ωτ ⁻collapse with the underground null results that exclude the parameter-free Markovian model.We give quantitative predictions for levitated nanospheres and matter-wave interferometry, sixfalsification conditions, and outline interpretive consequences: a classicality wavefrontdefining the present moment, a selective arrow of time, and dark energy as the unimodularaccumulation of collapse-injected energy.
This repository contains a short theoretical preprint proposing a phenomenological, local coarse-grained criterion for gravity-related loss of coherence in massive spatial superpositions. In the weak-field Newtonian regime we define a gravitational distinguishability densityρG(r)=∣∇Φ1(r)−∇Φ2(r)∣2/(8πG)ρG(r)=∣∇Φ1(r)−∇Φ2(r)∣2/(8πG)and argue that any collapse criterion based on local coarse-graining over a fixed length scale ℓℓ predicts a robust scaling signature: for large separations d≫Rd≫R (object radius), the coherence time saturates, τ(d)→constτ(d)→const, whereas the Penrose–Diósi global self-energy criterion predicts τPD(d)∝dτPD(d)∝d.The manuscript emphasizes falsifiability via a scaling test of τ(d)τ(d) at fixed mass and size, and includes a reproducible script/figure illustrating the contrasting asymptotic behaviors.
Time Cosmology (TC) reads the dark sectors as tenses and identifies the present with an irreversible selection performed by the fundamental forces. At the background and recent-universe level TC is observationally degenerate with quintessence. This paper exhibits the program's first non-cosmological discriminant. Carried to the laboratory, the irreversible recording of an outcome into the gravitational ledger is governed by the Penrose energy-time criterion tau ~ hbar/E_G, a parameter-free collapse time for spatial superpositions; TC supplies the ontological reason Penrose left open (collapse = writing to the past) and attaches a Landauer cost. Because TC selection is a quantum non-demolition (QND) measurement by the existing forces, not a stochastic noise field, it carries no continuous momentum diffusion and hence no spontaneous radiation; it therefore survives the 2021 Gran Sasso experiment that excluded the parameter-free Diosi-Penrose model. The prediction is falsifiable: a spatial superposition of ~1e-17 to 1e-15 kg held beyond tau must collapse; the gap to capability is ~6 orders of magnitude for second-scale experiments, shrinking to ~1-2 orders for long-hold MAQRO-class proposals. Scope is stated explicitly: the collapse time reproduces Penrose's (the novelty is the grounding and the non-radiative survival); the non-radiativity rests on strict non-stochasticity, with a residual-diffusion bound left as the central open calculation; the test is not within current reach. All numerical claims are reproduced by the archived code included in this record. Companion records: Indispensable Present (10.5281/zenodo.20707004), N3 (10.5281/zenodo.20564003), N5 calorimeter (10.5281/zenodo.20617808).
The Diósi-Penrose (DP) objective collapse model faces a severe empirical crisis, as recent underground experiments have definitively ruled out spontaneous bremsstrahlung radiation predicted by its stochastic noise mechanism. In this paper, we resolve this radiation paradox by proposing "Geometric Yielding"—a deterministic spacetime phase transition. Operating within the weak-field limit, we posit that spatial superposition collapses instantaneously when its quantum expansion pressure exceeds the structural threshold of the local linearized metric (LcL_cLc​), dissipating energy into spacetime curvature without electromagnetic coupling. Crucially, to resolve the singularity of point-like collapse, we anchor the ultimate lower bound of this localization (L0L_0L0​) in the discrete geometry of Loop Quantum Gravity(LQG). We propose that the collapse is stopped at the minimum volume eigenvalue of a spin network node, scaling with the Barbero-Immirzi parameter (γ\gammaγ) and the Planck length (ℓP\ell_PℓP​). This fundamental reduction in spectral dimension establishes a deterministic sawtooth-like dynamical cycle (τ\tauτ). For macroscopic objects, this cycle frequency is infinitely rapid, trapping them in a classical state via a self-induced Quantum Zeno effect. As a definitive empirical signature, we predict that for a 106 AMU10^6\text{ AMU}106 AMU silicon nanosphere, this Geometric Yielding will manifest itself as a Heaviside step-like suppression of interference visibility at a critical superposition distance (9.5μm9.5\mu\text{m}9.5μm), fundamentally distinguishing our model from the exponential decay predicted by continuous spontaneous localization (CSL) models.
Models of spontaneous wave function collapse have been postulated to address the measurement problem in quantum mechanics. Their primary function is to convert coherent quantum superpositions into incoherent ones, with the result that macroscopic objects cannot be placed into widely separated superpositions for observably prolonged times. Many of these processes will also lead to loss of coherence in neutrino oscillations, producing observable signatures in the flavor profile of neutrinos at long travel distances. The majority of studies of neutrino oscillation coherence to date have focused on variants of the continuous state localization model, whereby an effective decoherence strength parameter is used to model the rate of coherence loss with an assumed energy dependence. Another class of collapse models that have been proposed posit connections to the configuration of gravitational field accompanying the mass distribution associated with each wave function that is in the superposition. A particularly interesting and prescriptive model is Penrose’s description of gravitational collapse which proposes a decoherence time τ determined through E g τ ∼ ℏ , where E g is a calculable function of the Newtonian gravitational potential. Here we explore application of the Penrose collapse model to neutrino oscillations, reinterpreting previous experimental limits on neutrino decoherence in terms of this model. We identify effects associated with both spatial collapse and momentum diffusion, finding that the latter is ruled out in data from the IceCube South Pole Neutrino Observatory so long as the neutrino wave packet width at production is σ ν , x ≤ 2 × 10 − 12 m . Published by the American Physical Society 2024