Evidence of Nuclear-Scale Gravitational Decoherence as a Fundamental Lower Bound for Advanced Interferometric Detectors and Consistency with LISA Pathfinder
The sensitivity of current gravitational wave detectors (LIGO, VIRGO, KAGRA) in the low-frequency band (10-40 Hz) is limited by a persistent noise floor. In this Letter, we propose a phenomenological analysis based on the Diósi-Penrose (DP) model of gravitational decoherence. By treating the spatial cutoff parameter Rc as a free variable and fitting the theoretical displacement noise to the observed LIGO O3 sensitivity limit at 30 Hz, we derive a value of Rc ≈ 2.8 × 10^-15 m. This striking coincidence with the nuclear length scale suggests that semiclassical gravity couples to the discrete nuclear mass distribution. We demonstrate that this model correctly predicts the geometric scaling (1/L) observed between LIGO and VIRGO and, crucially, predicts an identical fundamental noise floor for KAGRA despite its different mirror material (Sapphire) and cryogenic operating temperature (20 K). This implies that the observed limit is material-invariant and represents a fundamental property of spacetime granularity interacting with matter.
The sensitivity of current gravitational wave detectors (LIGO, VIRGO, KAGRA) in the low-frequency band (10-40 Hz) is limited by a persistent noise floor. In this Letter, we propose a phenomenological analysis based on the Diósi-Penrose (DP) model of gravitational decoherence. By treating the spatial cutoff parameter Rc as a free variable and fitting the theoretical displacement noise to the observed LIGO O3 sensitivity limit at 30 Hz, we derive a value of Rc ≈ 2.8 × 10^-15 m. This striking coincidence with the nuclear length scale suggests that semiclassical gravity couples to the discrete nuclear mass distribution. We demonstrate that this model correctly predicts the geometric scaling (1/L) observed between LIGO and VIRGO and, crucially, predicts an identical fundamental noise floor for KAGRA despite its different mirror material (Sapphire) and cryogenic operating temperature (20 K). This implies that the observed limit is material-invariant and represents a fundamental property of spacetime granularity interacting with matter.
Levitated optomechanical systems are approaching the regime where macroscopic quantum superpositions become experimentally accessible. A central question is whether gravity itself, through its unavoidable coupling to material quantum fluctuations, imposes a fundamental decoherence channel on such superpositions. Starting from two independently well-tested physical elements—the quantum vacuum fluctuations of the material energy-momentum tensor, and the weak-field linear response kernel of classical general relativity—we derive a structurally rigid scaling law for the gravitational decoherence rate: \Gamma \propto G M^2 d^2 / (\hbar L^3) \cdot \Phi(l_*/L). The exponents and dependence on mass M, superposition separation d, and object size L are fixed entirely by dimensional analysis and the semiclassical field equations, without tunable parameters. The overall amplitude is set by a single phenomenological input—the ultraviolet cutoff scale l_* of the effective geometric noise. Identifying l_* with the Planck length yields \Phi \sim \mathcal{O}(1) and a decoherence rate of order 1\,\text{Hz} for nanoparticles with M \sim 10^{-14}\,\text{kg}, d \sim 10^{-7}\,\text{m}, and L \sim 10^{-6}\,\text{m}, placing the prediction within the foreseeable sensitivity window of next-generation levitated optomechanical setups. We provide explicit falsification conditions, a three-path staged verification strategy that does not require simultaneous optimisation of all parameters, and operational signatures—including a distinctive pure-dephasing channel without energy relaxation—that distinguish this mechanism from environmental noise, zero-temperature electromagnetic vacuum fluctuations, and the Diósi-Penrose model.
Laboratory-based experimental tests remain a central challenge in the study of the quantum-gravity interface. We present a quantitative, experimentally testable prediction for gravitationally induced quantum decoherence of spatial superpositions in levitated optomechanical systems. Starting from two independently well-tested physical elements—the quantum nature of material energy-momentum fluctuations (established in particle physics) and the linear response kernel of classical geometry (derived from the weak-field limit of general relativity and verified by gravitational-wave observations)—and supplementing them with a minimal extension postulate for superposition states, we obtain a rigid scaling law for the gravitational decoherence rate: \Gamma \sim G M^2 d^2 / (\hbar L^3) \cdot \Phi(l_*/L), where M is the mass of the object, d the spatial separation of the superposition branches, L the characteristic linear dimension, and \Phi a dimensionless function encoding the unknown ultraviolet cutoff scale l_* of the effective geometric noise. The structural form \Gamma \propto M^2 d^2 / L^3 contains no free adjustable parameters; the overall amplitude is set by the choice of l_*. Identifying l_* with the Planck length \ell_P = \sqrt{\hbar G / c^3}—the only known scale bridging quantum theory and gravity—yields \Phi \sim \mathcal{O}(1) and a specific numerical target. For current levitated nanoparticle experiments (M \sim 10^{-14}\,\text{kg}, d \sim 10^{-7}\,\text{m}, L \sim 10^{-6}\,\text{m}), this Planck-scale hypothesis predicts a decoherence rate of order 1\,\text{Hz}, placing it within the foreseeable sensitivity window of next-generation optomechanical setups. We discuss the exclusive physical signatures distinguishing this mechanism from environmental decoherence channels and outline explicit falsification conditions, providing experimental groups with a concrete target to probe the quantum-gravity interface in the laboratory.
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.
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 at ultra-low experimental temperatures (T≪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 ds of the macroscopic test mass determines the decoherence rate scaling, creating a new class of ultra-sensitive 'fracton-gravity sensors'.
Wave function collapse models postulate a fundamental breakdown of the quantum superposition principle at the macroscale. Therefore, experimental tests of collapse models are also fundamental tests of quantum mechanics. Here, we compute the upper bounds on the collapse parameters, which can be inferred by the gravitational wave detectors LIGO, LISA Pathfinder, and AURIGA. We consider the most widely used collapse model, the continuous spontaneous localization (CSL) model. We show that these experiments exclude a huge portion of the CSL parameter space, the strongest bound being set by the recently launched space mission LISA Pathfinder. We also rule out a proposal for quantum-gravity-induced decoherence.
Predictions of the Diósi–Penrose (DP) gravity-related collapse model depend strongly on the mass-density smoothing length R₀ and on the frequency spectrum of the gravitational fluctuations. We reanalyze the public low-energy electronic-recoil data of XENONnT (1–30 keV, 433 events, 1.16 t·yr) with an unbinned likelihood and report four results. First, when R₀ exceeds the atomic size, the equivalence principle makes the nucleus and its electrons accelerate together, and low-energy X-ray emission is strongly cancelled (about 2×10⁻⁴ at 1 keV and 0.16 at 10 keV for xenon). Including this screening, the bound on the white-noise DP model is R₀ > ~0.9 nm, much weaker than the unscreened value (~4.0 nm). Second, the reported bound R₀ > 2.8 nm of an earlier collapse analysis of XENONnT data appears to differ from the Majorana analysis in signal normalization by a factor π^(3/2). With the same normalization it corresponds to 1.56 nm, in agreement with the 1.52 nm we obtain under the same conditions. Third, an 'atomic-unit' variant, with R₀ set to the atomic radius and the fluctuation cutoff set to the electronic time scale, cannot be decided with these data: its verdict ranges from allowed (prediction/limit 0.006) to excluded (11) depending on how strongly the electrons co-move with the nucleus. Fourth, a parameter-free 'phonon-unit' variant, with both R₀ and the cutoff fixed by the lattice vibration of the same nucleus (Debye–Waller rms displacement and Debye frequency), passes the X-ray data independently of the screening treatment and predicts spontaneous heating of about 9.4 pW/kg in copper at cryogenic temperature. This lies just below the currently known unexplained heat-leak limit (~10 pW/kg). X-rays cannot separate the two variants; the (atomic mass × Debye temperature)^(3/2) heating scaling predicted by the phonon-unit variant can be tested by comparing heat leaks in tungsten and aluminium (a factor of about 16).“v2: removed comparison with a withdrawn preprint; added comparison with the XENON collaboration analysis (arXiv:2506.05507) and the 8π convention conversion.”