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引力诱导纠缠与坍缩模型:退相干率斜率符号判别(编号117)

Daicun Li

Published Oct 24, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.23611755

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•Oct 24, 2026•0 citations
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.
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We present a derivation of quantum decoherence rates within a vacuum pressure gradient model of gravity, in which local vacuum density decreases near massive objects according to rho_vac(r) = rho_0*(1 - 2GM/rc^2). This model predicts that decoherence rates are suppressed near massive objects — in direct opposition to the Diosi-Penrose model, which predicts enhancement near mass. The sign reversal produces a measurable fractional difference of 3GM/rc^2 between the two model predictions. We identify that quantum decoherence and macroscopic void decay are the same physical process at different scales, both governed by local vacuum bubble density eroding void-pair boundaries. We propose an experimental protocol using atomic interferometry at varying gravitational potentials, achievable with existing space-based platforms, that discriminates between this model and Diosi-Penrose by sign alone. For trapped ion qubits with coherence times of order 100 seconds, the predicted fractional improvement between Earth surface and the International Space Station is 8.22 x 10^-11.UFFT Paper #1. Part of the Unified Foam Field Theory (B + V = D). Zero free parameters. GitHub: https://github.com/WebEnvy/UnifiedFoamFieldTheory
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.
This study explores quantum effects in weak gravitational fields with the aim of identifying feasible pathways towards tabletop tests of quantum gravity. Using numerical simulations of matter-wave interference for nanoparticles with masses between and kg, we investigate how environmental and fundamental decoherence mechanisms shape observable signatures. The results reveal a mass-dependent reduction in interference visibility, dropping from near unity at kg to below 0.2 at kg. Coherence times were found to exceed one second for particles lighter than 10^(-16) kg under cryogenic ultra-high-vacuum conditions, but decreased to sub-millisecond scales for kg particles at room temperature, confirming thermal radiation as the dominant source of decoherence. In parallel, collapse models such as CSL predict additional suppression of visibility for interrogation times of 0.1 s, particularly for masses above kg, enabling discrimination between environmental and intrinsic decoherence mechanisms. These findings underscore the necessity of maintaining ultra-high vacuum and cryogenic environments to detect gravitationally induced quantum phases, thereby providing a practical framework for near-future interferometry experiments. While the present work is limited to phenomenological models and simulated data, it establishes a roadmap for extending investigations to heavier mass regimes, incorporating realistic noise sources, and testing alternative collapse scenarios.
We study idealized levitated protocols that create spatial superpositions of massive test particles. For each protocol, we compare the dimensionless contrast-loss exponent of mass-proportional continuous spontaneous localization (CSL) with the Diósi--Penrose (DP) self-energy exponent EGτ/ℏE_Gτ/\hbarEG​τ/ℏ. We first prove that the point-particle CSL separation kernel has an exact random-unitary realization: Gaussian momentum kicks arriving at Poisson-distributed times produce the same unconditional decay of spatial coherence, although a pure state conditioned on the complete kick record remains pure. The separation kernel alone therefore specifies an operational decoherence law, not the occurrence of objective collapse. We then show that the ratio of the CSL and DP exponents is independent of particle mass and interrogation time. In the point-particle model it depends only on branch separation and an effective distance; for the standard GRW reference parameters, its resolved-superposition crossover is x∗≈1.91 nmx_*\approx1.91\,\mathrm{nm}x∗​≈1.91nm. For rigid spherical bodies with an arbitrary normalized radial mass profile, total mass, overall density scale, and interrogation time again cancel, leaving a dimensionless geometry factor. The results distinguish three requirements for a decisive experiment: detectable absolute effects, a controlled comparison of CSL and DP scales, and observables capable of discriminating physically different dynamics that share the same ensemble decoherence kernel.
In linear open-quantum-system dynamics, the off-diagonal coherence of a spatially superposed source mass decays with a visibility envelope that is independent of the prepared relative phase between the two position amplitudes. This phase-blindness is a direct consequence of linearity: unitary and Lindblad generators commute with global phase rotations on the source branch, and the interference fringe takes the form P(φ,t) = ½[1 + v(t) cos φ] with v(t) = exp(−Γt). We propose a phase-scanning protocol to test this null hypothesis in a BMV-type nanodiamond interferometer. We parametrize a first-harmonic deviation by writing v(φ,t) = exp[−Γ₀t − Γ₁t(1 + η cos(φ − φ₀))], so that η = 0 recovers linear dynamics and η ≠ 0 signals phase-sensitive decoherence. No existing Markovian collapse model predicts η ≠ 0; the parameter is therefore a phenomenological null-test axis. For illustrative BMV target parameters (m = 10⁻¹⁴ kg, d = 250 μm, T = 10 mK) and a reference scale Γ₁ = 0.127 s⁻¹, idealized scaling gives η = 0.05 reachable at ~7 × 10⁴ shots and η = 0.01 at ~2 × 10⁶ shots for SNR = 3 at t = 1 s. The protocol bounds phase sensitivity, not the overall collapse rate, and is proposed, not demonstrated. I. Introduction The superposition principle is the structural core of quantum mechanics, yet its compatibility with gravitation remains untested in the regime where both the spatial extent of a superposition and its mass are macroscopically large. Proposals to prepare and interferometrically close spatial superpositions of massive nanoparticles—most prominently the BMV scheme [1,2]—have motivated experiments aimed at observing gravitationally mediated entanglement and at bounding exotic decoherence. In parallel, dynamical-collapse models [3,4] predict deviations from unitary evolution whose magnitude scales with mass and separation, and matter-wave interferometry has long been used to bound their parameters [5,6].