A model of the vacuum as a face-centered-cubic lattice predicts a two-step quantum–classical threshold, at 13.1 and 22.6 µg, from the hypothesis that a center-of-mass excitation stays coherent only while its reduced Compton wavelength is resolvable by the lattice. Collapse models also limit macroscopic coherence, so the two must be told apart by more than a scale. We derive three discriminators from the model's postulates and compute the counterpart in Diósi–Penrose collapse and in continuous spontaneous localization (CSL). The thresholds depend on total mass alone, while both collapse models depend on density. Below 13.1 µg the model predicts no intrinsic decoherence, where collapse takes 1 s for Diósi–Penrose and about a microsecond for CSL at its experimental bound, for 10⁻¹⁵ kg over 1 µm. The model predicts no measurable heating; read as position localization, its own rate scale would exceed the LISA Pathfinder bound by 66 orders of magnitude, so coherence loss above the threshold must be dephasing in the energy basis. If its effective mode mass is the relevant mass, a 16.2 µg mechanical cat state then bounds the irreversible coupling at 38 orders below its natural scale. A worked levitated-particle example and a public script complete the analysis.
A model of the vacuum as a face-centered-cubic lattice predicts a two-step quantum–classical threshold, at 13.1 and 22.6 µg, from the hypothesis that a center-of-mass excitation stays coherent only while its reduced Compton wavelength is resolvable by the lattice. Collapse models also limit macroscopic coherence, so the two must be told apart by more than a scale. We derive three discriminators from the model's postulates and compute the counterpart in Diósi–Penrose collapse and in continuous spontaneous localization (CSL). The thresholds depend on total mass alone, while both collapse models depend on density. Below 13.1 µg the model predicts no intrinsic decoherence, where collapse takes 1 s for Diósi–Penrose and about a microsecond for CSL at its experimental bound, for 10⁻¹⁵ kg over 1 µm. The model predicts no measurable heating; read as position localization, its own rate scale would exceed the LISA Pathfinder bound by 66 orders of magnitude, so coherence loss above the threshold must be dephasing in the energy basis. If its effective mode mass is the relevant mass, a 16.2 µg mechanical cat state then bounds the irreversible coupling at 38 orders below its natural scale. A worked levitated-particle example and a public script complete the analysis.
We model the vacuum as a discrete face-centered-cubic (K=12) tensor network with Bell-pair bonds and use it to predict a two-step quantum-to-classical threshold for macroscopic center-of-mass superpositions. A reversible dispersive deformation of the center-of-mass mode sets in at msoft≈13.1μg, and coherence becomes geometrically unsustainable at mhard≈22.6μg. The two scales are separated by the exact, parameter-free ratio 3, fixed by the edge-to-circumradius ratio of the cuboctahedral triangular face. Gravitational-collapse models predict a single scale of the same order, so the distinctive, falsifiable content is the two-step structure and the exact 3 separation, testable by a mass scan across the window; the recent 16.2μg cat-state oscillator of Bild et al. falls between the thresholds, where coherence is not ruled out. The absolute window depends on the bond length L=4ln2ℓP≈1.665ℓP, fixed by one calibration against the Bekenstein–Hawking area law. This calibration and the Compton representability hypothesis—that a mass excitation remains coherent only while its reduced Compton wavelength is resolvable by the lattice—are stated model inputs rather than derivations, motivated by the Compton frequency internal clock of massive excitations, the mass cutoff generic to lattice-regularized field theories, and the total-mass dependence observed in composite-object interferometry. Open problems are stated explicitly.
Quantum mechanics, which governs all microscopic phenomena, encounters challenges when applied to macroscopic objects that exhibit classical behavior. To address this micro-macro disparity, collapse models such as the Continuous Spontaneous Localization (CSL) and Diosi-Penrose (DP) models have been proposed. These models phenomenologically modify quantum theory to reconcile its predictions with the observed classical behavior of macroscopic systems. Based on previous works\,([Phys.\,Rev\,D,\,95(8):084054\,(2017)] and [Phys.\,Rev.\,D,\,94:124036,\,(2016)]), an improved bound on the collapse model parameters is given using the updated acceleration noise data released from LISA Pathfinder\,([Phys.\,Rev.\,D, 110(4):042004,\,(2024)]). The CSL collapse rate is bounded to be at most λCSL≤8.3×10−11\,s−1 at the mili-Hertz band when rCSL=10−7m, and the DP model's regularization cut-off scale is constraint to be σDP∼285.5\,fm. Furthermore, we discuss the potential advantages of using deep-underground laboratories to test these quantum collapse models. Our results show the quiet seismic condition of the current deep-underground laboratory has the potential to further constrain the CSL collapse model to λCSL≤3×10−11s−1 when rCSL=10−7m.
Spontaneous collapse models are phenomological theories formulated to address major difficulties in macroscopic quantum mechanics. We place significant bounds on the parameters of the leading collapse models, the continuous spontaneous localization (CSL) model, and the Diosi-Penrose (DP) model, by using LISA Pathfinder's measurement, at a record accuracy, of the relative acceleration noise between two free-falling macroscopic test masses. In particular, we bound the CSL collapse rate to be at most $(2.96\ifmmode\pm\else\textpm\fi{}0.12)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. This competitive bound explores a new frequency regime, 0.7 to 20 mHz, and overlaps with the lower bound ${10}^{\ensuremath{-}8\ifmmode\pm\else\textpm\fi{}2}\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ proposed by Adler in order for the CSL collapse noise to be substantial enough to explain the phenomenology of quantum measurement. Moreover, we bound the regularization cutoff scale used in the DP model to prevent divergences to be at least $40.1\ifmmode\pm\else\textpm\fi{}0.5\text{ }\text{ }\mathrm{fm}$, which is larger than the size of any nucleus. Thus, we rule out the DP model if the cutoff is the size of a fundamental particle.
The transition from the quantum to the classical realm remains one of the most profound open questions in physics. While quantum theory predicts the existence of macroscopic superpositions, their apparent absence in the everyday world is attributed either to environmental decoherence or to an intrinsic mechanism for wave-function collapse. This work presents a quantitative and experimentally grounded framework for distinguishing these possibilities. We propose a levitated optomechanical platform capable of generating controllable Schrodinger-cat states in the center of mass motion of a dielectric nanosphere. A comprehensive master equation incorporates gas collisions, black-body radiation, and photon-recoil noise, establishing a calibrated environmental baseline. The Continuous Spontaneous Localization (CSL) model is embedded within the same framework, predicting a characteristic saturation of the decoherence rate with superposition size and a quadratic scaling with mass. A Bayesian inference protocol is outlined to discriminate collapse induced excess decoherence from environmental noise. Together these elements provide a concrete experimental blueprint for a decisive test of quantum linearity, either revealing new physics beyond standard quantum mechanics or setting the most stringent bounds to date on objective-collapse parameters.
This memo addresses a question: In the “substrate field–soliton” model (v2 paper), canthe intuition “observation collapse = irreversible physical process” be realized as a concretedynamical collapse model? The answer is yes, but with a decisive number attached. Weprove that: (i) The master equation driven by the noise naturally derived from the masscoupling m(ϕ) is structurally isomorphic to the CSL (Continuous Spontaneous Localization) model, and the two ad hoc assumptions of CSL—mass-weighted coupling and positionbasis—are no longer assumptions in this model, but corollaries of the equivalence principleand the mass density operator; (ii) The collapse rate is proportional to Newton’s constant,Γ ∝ Gm2, realizing the motivation of the Di´osi–Penrose program that “collapse strengthis given by gravity,” though the mechanism is different (substrate noise rather than spacetime superposition instability); (iii) Decisive verdict: If the noise is taken as the quantumvacuum fluctuation of ϕ, the single-nucleon collapse rate is ∼ 10−28 s−1, which is 12 orders of magnitude smaller than the value required by GRW—the pure quantum fluctuationversion cannot solve the measurement problem. To achieve true collapse, “intrinsic probability” must be interpreted as a classical true-random component of the substrate condensate,whose power D becomes a new free parameter. In this case, the model becomes a CSL witha specific mediating field, and its heating rate directly interfaces with existing experimentalconstraints (X-ray spontaneous emission, cantilever noise, LISA Pathfinder). We presenta complete parameter space analysis, including the “localization-heating squeeze” identityP/λ = ℏ2/(2m0rC2), which explains why models with rC ∼ 1 fm are strictly ruled out, whilethose with rC ∼ 10−7 m survive.
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/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∗≈1.91nm. 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.