Stochastic semiclassical gravity represents stress--energy fluctuations through the Einstein--Langevin noise kernel. We examine its Newtonian projection for specified closed, particle-number-conserving non-relativistic sources and distinguish the source covariance from a reduced matter channel. The connected one-particle covariance is state dependent and differs from the universal potential-noise law postulated in the Diósi--Penrose model. To relate the source spectrum to dephasing, we define a separate static probe subject to a prescribed Gaussian noise law. For a finite-variance source operator in an isolated non-degenerate eigenstate, the full connected spectral measure has a gap around zero. The probe dephasing exponent is then bounded and its long-time slope vanishes. Stationary doublets can instead carry static or low-frequency spectral lines, while a specified freely spreading Gaussian source gives a finite limiting exponent. Continuum results depend on preparation, normalisation, infrared regularisation and the order of limits. We also compare coherent and incoherent many-body preparations and establish no-signalling for fixed classical-noise channels. These results identify the spatial, temporal and dynamical assumptions needed to relate source fluctuations to a matter-decoherence model. They do not exclude Markovian limits in other number-conserving non-relativistic preparations.
Stochastic semiclassical gravity represents stress--energy fluctuations through the Einstein--Langevin noise kernel. We examine its Newtonian projection for specified closed, particle-number-conserving non-relativistic sources and distinguish the source covariance from a reduced matter channel. The connected one-particle covariance is state dependent and differs from the universal potential-noise law postulated in the Diósi--Penrose model. To relate the source spectrum to dephasing, we define a separate static probe subject to a prescribed Gaussian noise law. For a finite-variance source operator in an isolated non-degenerate eigenstate, the full connected spectral measure has a gap around zero. The probe dephasing exponent is then bounded and its long-time slope vanishes. Stationary doublets can instead carry static or low-frequency spectral lines, while a specified freely spreading Gaussian source gives a finite limiting exponent. Continuum results depend on preparation, normalisation, infrared regularisation and the order of limits. We also compare coherent and incoherent many-body preparations and establish no-signalling for fixed classical-noise channels. These results identify the spatial, temporal and dynamical assumptions needed to relate source fluctuations to a matter-decoherence model. They do not exclude Markovian limits in other number-conserving non-relativistic preparations.
Quantum processors encode computational information in relative phases and are therefore sensitive to spatially and temporally correlated dephasing. We formulate gravitational redshift as a physically constrained template for such noise. A fixed, known redshift produces a deterministic phase, whereas dephasing arises only when unresolved displacement, timing, or frequency fluctuations are transduced into phase uncertainty; for vertical motion, the conversion factor is β g = ω 0 g / c 0 2 . The gravity-specific content is thus the mapping from geometry fluctuations to phase covariance and frequency-noise spectra, while the resulting Gaussian dephasing dynamics are generic. We test spatial-kernel dependence using exponential, Gaussian, Matérn, and power-law correlations. Circuit-level effects are evaluated with an explicit GHZ-preparation circuit, showing that a full-GHZ-per-layer exponential approximation overestimates loss. For temporal correlations, we derive S δ ω = β g 2 S h and use a mechanically motivated drift-plus-vibration model, which attributes memory to the mechanical process rather than gravity. Platform estimates indicate that the gravity-transduced contribution is negligible compared with present technical dephasing. The framework therefore provides a falsifiable geometry-to-noise model while keeping mitigation and compilation claims quantitatively cautious.
A gravitationally induced loss of matter coherence is the most-discussed empirical window on the quantum–gravity interface, and a recurring claim is that its shape — most often a short-time Gaussian onset |ρ₀₁(T)| = e^(−½(T/τ_G)²), as in finite-memory variants of the Diósi–Penrose proposal — diagnoses the underlying mechanism (non-Markovianity, state-dependence, or a genuinely quantum-gravitational record process). We prove the opposite, in a sharp and useful form: the gravitational dephasing curve is mechanism-blind, and the structural distinction that would mark a quantum-gravitational record process is not a function of the reduced channel. Three results, each computed at high precision. (i) The Gaussian onset is not a signature: a state-independent, irreversible record commitment ("seal") firing at a ramping hazard λ(t) = a·t reproduces it exactly (|ρ₀₁(T)| = e^(−aT²/2), residual 0), and a constant hazard gives the pure exponential semigroup — the most Markovian channel there is. (ii) Any state-independent irreversible seal is CP-divisible: |ρ₀₁(T)| = e^(−∫₀ᵀλ) is monotone, so it can never produce revivals; revivals occur exactly for Gaussian kernels whose running integral goes negative — the underdamped (still spectrally positive) kernel is the canonical case, with the boundary at ω₀τ = 3.644173671645632… — a non-Markovianity orthogonal to the structural axis. (iii) Operational undecidability from the dephasing curve: a continuous (Ornstein–Uhlenbeck) classical-noise ontology and a matched sparse-seal record ontology produce bit-identical free-induction coherence |ρ₀₁(T)| for all T (the identity ∫λ_OU = χ is sympy-exact; an independent numerical integration gives the machine-zero residual max|C_OU − C_seal| = 7.1×10⁻¹⁰²), so free-induction decay cannot separate them. Multi-time dynamical decoupling (echo/CPMG) can probe reversibility — it distinguishes a refocusable noise from an irreversible commitment — but the genuine quantum-gravitational content, whether the matter's closed-system record process is indivisible in Barandes' sense / unrefinable in the sealed-record sense, is structural (the off-diagonal support of the decoherence functional between sparse commitments) and is invisible to passive reduced-channel measurement, at every order, because a bath dilation is always divisible and a closed unitary system is indivisible yet a trivial channel (an invasive protocol that reconstructs Γ(t) would insert a seal at each conditioning step, and so cannot certify the unintervened process). We make the structural axis precise, exhibit the consistent-histories functor that turns "unrefinable ⟺ indivisible" into a theorem at the kinematic level, and isolate the one open obligation (whether the gravitational record process is sparsely or continuously sealing). The widely used finite-memory Diósi–Penrose-family kernel is, on this analysis, one illustrative CP-divisible member of the undecidable class rather than a discriminating prediction. The practical upshot is a sharpened no-go: a free-induction onset-shape measurement, however precise, does not distinguish gravitational quantum decoherence from classical gravitational noise — the reversibility of the mechanism is probed only by multi-time decoupling, and the structural indivisibility that would mark a genuinely quantum-gravitational record process is reachable by no reduced-channel measurement at all.
Abstract We show that general relativistic time dilation can act as a controllable source of non-Markovianity in the dynamics of delocalized quantum clocks coupled to structured environments. As a concrete setting, we model a delocalized quantum clock, a two-level Unruh-DeWitt detector interacting with a thermal scalar field with finite correlation time in a weak, static gravitational field. The gravitational redshift between spatially sepa- rated branches leads to a path-dependent sampling of the bath correlation functions and to an effective spectral mismatch between the arms of the interferometer. Within a second-order time-convolutionless expansion we derive a time-local master equation whose time-dependent rates depend explicitly on the redshift parameter and reduce to the usual Markovian Gorini-Kossakowski-Sudarshan-Lindblad generator when gravity is switched off or the bath becomes memoryless. Numerical evaluation for an Ohmic environment reveals gravitationally in- duced coherence revivals and information backflow, providing a genuine non-Markovian signature that can be quantified by standard trace-distance measures. We identify a resonance-like regime in which the gravitational detuning becomes comparable to the dominant bath frequencies, leading to a suppression of decoherence and an enhancement of entanglement lifetimes relative to the flat-space Markovian case. Finally, by comparing the size of the gravity-induced deviations to quantum projection noise in state-of-the-art optical clocks, we derive an analytic signal-to-noise ratio and show that, within our model, engineered low-frequency reservoirs could al- low gravity-controlled memory effects to be resolved above the shot-noise limit on few-hour integration times, whereas for fast thermal baths the effect remains QPN-limited and effectively unobservable.
We formulate the gravitationally induced quantum decoherence of a massive object prepared in a spatial superposition. Starting from linearized gravity coupled to a massive system particle and an environmental scalar field, we derive a closed-time-path influence functional governing the reduced system dynamics. In the nonrelativistic and quasi-static regime, the decoherence exponent can be written as a bilinear functional of the difference of the system stress-energy tensors and an effective noise kernel obtained by dressing the environmental stress-energy tensor correlator with graviton propagators. We then apply this framework to the Newtonian long-range gravitational interaction and evaluate the resulting decoherence function for a dilute nonrelativistic gas modeled by finite wave packets and coarse-grained in time and space. By performing controlled approximations, we obtain analytic expressions for the cumulative decoherence function and show that the dominant contribution is accumulated logarithmically over a broad range of distances, while remaining subdominant to conventional collisional decoherence under realistic conditions.
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.
It has already been suggested that quantum theory needs to be reformulated or modified in order to explain the measurement process and the successive collapse of the wave- function. However, there are also models of another type which keep quantum theory intact and instead modify the classical gravity by introducing stochasticity to it. These models suggest that there is a fluctuation in the background gravitational field which eventually results in the decoherence of the wavefunction. These fluctuations limit the precision with which one can measure the properties of a spacetime geometry with a quantum probe. Two similar models along this line have been suggested by Karolyhazy (K-model) and Diósi(D-model). They are based upon apparently different spacetime bounds. The results obtained for the coherence length are also somewhat different. In this article, we show that, given certain conditions apply, the minimal spacetime bounds in these two models are equivalent. We also derive the two-point correlation for the fluctuation potential in K-model which turns out to be non-white, unlike in D-model, where the corresponding correlation is white noise in time. In our opinion, this is the origin of discrepancy in the predictions of the two models. We argue that the noise correlation cannot be determined uniquely from a given spacetime bound.