This note asks what a threshold picture of objective collapse predicts for Bose–Marletto–Vedral (BMV) tests of gravity-mediated entanglement. A collapse rate that switches on sharply violates complete positivity. For homogeneous spheres, Markovian Diósi–Penrose (DP) collapse forbids BMV entanglement at all times. If the threshold is instead modeled as a build-up in time, using Ornstein–Uhlenbeck colored DP noise with correlation time τ_c, the dynamics stays completely positive and evades the non-interferometric bounds we considered for τ_c ≳ 1.7×10³ s. Colored CSL cannot do this. The prediction is transient entanglement, which rises, peaks and vanishes at about 1.46×10⁻³ τ_c. The time profile alone matches slow classical noise. A superposition-size scan of about 90 single-mass runs separates the two. The window requires a heavier effective collapse threshold and closes under minimal-measurement-time criteria. This is a modest, testable prediction, not evidence for collapse. Computations assisted by AI tools.
This note asks what a threshold picture of objective collapse predicts for Bose–Marletto–Vedral (BMV) tests of gravity-mediated entanglement. A collapse rate that switches on sharply violates complete positivity. For homogeneous spheres, Markovian Diósi–Penrose (DP) collapse forbids BMV entanglement at all times. If the threshold is instead modeled as a build-up in time, using Ornstein–Uhlenbeck colored DP noise with correlation time τ_c, the dynamics stays completely positive and evades the non-interferometric bounds we considered for τ_c ≳ 1.7×10³ s. Colored CSL cannot do this. The prediction is transient entanglement, which rises, peaks and vanishes at about 1.46×10⁻³ τ_c. The time profile alone matches slow classical noise. A superposition-size scan of about 90 single-mass runs separates the two. The window requires a heavier effective collapse threshold and closes under minimal-measurement-time criteria. This is a modest, testable prediction, not evidence for collapse. Computations assisted by AI tools.
In the Bose–Marletto–Vedral (BMV) class of tabletop gravity experiments, two mesoscopic masses are each placed in a spatial superposition and their Newtonian interaction is used as a witness of gravitationally induced entanglement. Aspelmeyer [5] has sharpened the standard argument: observing entanglement at the 10-15 kg scale already rules out current Diósi–Penrose (DP) collapse models. Here we ask a complementary question: when the source mass itself is the object in superposition, what is the sign of the gravity-induced decoherence *rate* as a function of M/r (mass over characteristic superposition scale), and where in the mass range is that rate actually measurable? We compare three branches: (A) linearized quantum field theory, which gives reversible phase accumulation and Gamma = 0; (B) DP / continuous spontaneous localization (CSL) collapse, for which Gamma > 0 and grows steeply with M/r (positive trend); and (C) a phenomenological strawman of variable vacuum-foam / stochastic-spacetime suppression, Gammafoam = Gammafbg exp(-3 kappa GM/(rc2)), for which the trend is negative. Branch C is not derived from any specific quantum-gravity model; it is introduced only to give the sign question a non-trivial alternative. We solve the rates for a uniform sphere (density rho = 2000 kg/m3, superposition separation d = 10 r) and find: (i) a rate-resolved window M ~ 2×10-16 to 10-14 kg in which the DP rate exceeds a BMV-class environmental floor of 0.05 s-1 but is still measurable — this window lies below the regime where entanglement-survival alone, à la Aspelmeyer, already excludes DP; (ii) the phenomenological strawman foam-suppression branch is observationally degenerate with QFT-zero on Earth, because d ln Gammafoam / d ln M = -2 kappa GM/(rc2) ~ -10-37 to -10-35 across the entire lab range. Discriminating this toy from QFT-zero would require the near-Schwarzschild regime x = GM/(rc2) ~ O(1). Shot-noise-limited run counts are ~6 at M = 10-15 kg, ~104 at M = 10-16 kg, and environment-limited below M = 10-16 kg. All numerical values are illustrative/synthetic order-of-magnitude estimates.
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.
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.
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.
We develop a low-energy, Newtonian-limit effective field theory (EFT) describing gravitationally induced decoherence arising from a classical stochastic gravitational channel. The framework is formulated as completely positive, Markovian Lindblad dynamics coupled to the mass-density operator with spatially correlated white noise. We derive scaling laws for single-mass superpositions and for two-mass Bose–Marletto–Vedral (BMV) configurations, identify four universal parametric regimes, and construct a model-independent testability window in the parameter space of noise strength and correlation length. Our results provide a direct operational link between laboratory-scale entanglement experiments and foundational questions concerning the quantum or classical nature of gravity.