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Gravitational Decoherence of Entanglement in Non-Separable Temporal Bubbles: NSTB Dynamics in a Schwarzschild Background

Thierry Marechal

Published Mar 22, 2026• 0 citations
Publisher

Abstract

If gravity and entanglement share a common origin in the temporal flow rate field τ(x), then gravitational tidal fields should produce measurable decoherence of entanglement. This paper derives the first quantitative prediction for this effect. We construct the dynamics of a Non-Separable Temporal Bubble (NSTB) — the shared temporal configuration of two entangled particles — in a Schwarzschild gravitational background. The bubble's internal coherence field satisfies a wave equation with a tidal potential proportional to the second derivative of the background τ-field. Linearization yields a visibility reduction for entanglement: ΔV = GM d² / (c² r³ f_intrinsic) where d is the spatial extent of the bubble (the separation between entangled particles), r the distance from the gravitating mass, and f_intrinsic the internal frequency set by the fractal-temporal hierarchy. The key signature is the tidal scaling ∝ d²/r³, which uniquely distinguishes NSTB from competing gravitational decoherence proposals: Penrose-Diósi predicts mass-dependent decoherence (different observable), Ralph-Pienaar predicts gradient scaling ∝ d/r² (different power law), and standard QFT in curved spacetime predicts no decoherence at all (zero). Any observed gravitational decoherence of entanglement with d²/r³ scaling would therefore constitute direct evidence for a shared origin of gravity and quantum correlations. For Earth-orbit experiments with optical photons (d ~ 400 km, f ~ 10¹⁴ Hz), the predicted effect is ΔV ~ 10⁻²⁷ — far below current sensitivity. Near a neutron star with microwave-frequency entanglement (d ~ 100 km, f ~ 10¹⁰ Hz), the effect grows to ~ 10⁻¹⁰, within conceivable reach of future space-based quantum networks. Three enhancement strategies are identified: stronger tidal fields, larger bubble separations, and lower-frequency entangled states. The prediction closes an open parameter problem from the companion entanglement paper (κ = 1, f_bubble = f_photon) and establishes a concrete, falsifiable target for the emerging field of gravitational quantum experiments.

DOI
10.5281/zenodo.19163137

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If gravity and entanglement share a common origin in the temporal flow rate field τ(x), then gravitational tidal fields should produce measurable decoherence of entanglement. This paper derives the first quantitative prediction for this effect. We construct the dynamics of a Non-Separable Temporal Bubble (NSTB) — the shared temporal configuration of two entangled particles — in a Schwarzschild gravitational background. The bubble's internal coherence field satisfies a wave equation with a tidal potential proportional to the second derivative of the background τ-field. Linearization yields a visibility reduction for entanglement: ΔV = GM d² / (c² r³ f_intrinsic) where d is the spatial extent of the bubble (the separation between entangled particles), r the distance from the gravitating mass, and f_intrinsic the internal frequency set by the fractal-temporal hierarchy. The key signature is the tidal scaling ∝ d²/r³, which uniquely distinguishes NSTB from competing gravitational decoherence proposals: Penrose-Diósi predicts mass-dependent decoherence (different observable), Ralph-Pienaar predicts gradient scaling ∝ d/r² (different power law), and standard QFT in curved spacetime predicts no decoherence at all (zero). Any observed gravitational decoherence of entanglement with d²/r³ scaling would therefore constitute direct evidence for a shared origin of gravity and quantum correlations. For Earth-orbit experiments with optical photons (d ~ 400 km, f ~ 10¹⁴ Hz), the predicted effect is ΔV ~ 10⁻²⁷ — far below current sensitivity. Near a neutron star with microwave-frequency entanglement (d ~ 100 km, f ~ 10¹⁰ Hz), the effect grows to ~ 10⁻¹⁰, within conceivable reach of future space-based quantum networks. Three enhancement strategies are identified: stronger tidal fields, larger bubble separations, and lower-frequency entangled states. The prediction closes an open parameter problem from the companion entanglement paper (κ = 1, f_bubble = f_photon) and establishes a concrete, falsifiable target for the emerging field of gravitational quantum experiments.
What if the mystery of quantum entanglement—Einstein’s famous "spooky action at a distance"—could be understood through shared temporal structures rather than superluminal signals? This paper explores the quantum foundations sector of Temporal Texture Gravity, introducing a candidate mechanism called the "Non-Separable Temporal Bubble". It investigates how entangled particles might share a single, spatially extended temporal configuration that coordinates their measurement outcomes while remaining strictly non-signaling at the observable level. The paper frames this mechanism with complete transparency, outlining both its mathematical predictions and its current boundaries: A Shared Temporal Substrate: Proposes that entangled particles are connected through an extended temporal bubble. Under standard quantum probability rules, this shared substrate exactly reproduces quantum correlation laws and the famous Tsirelson bound for quantum measurement limits. Strict No-Signaling Discipline: Addresses the fundamental requirement that quantum correlations must never allow faster-than-light communication. The paper documents an internal refutation of an earlier model version that leaked information, establishing the exact mathematical conditions required to keep hidden non-local states completely unreadable to outside observers. Gravitational Test Signatures: Examines how quantum bubbles interact with gravitational curvature (such as around black holes or massive bodies). The paper derives three distinct structural signatures—a "magic angle" where tidal distortions cancel out, an isotropy null where symmetric bubbles decouple, and a clear separation between phase shifts and visibility loss. Presented as an exploratory candidate extension rather than a derived result of the core action, this paper establishes a rigorous roadmap for bridging temporal geometry with quantum non-locality.
This manuscript develops three concrete, falsifiable predictions based on a framework in which time and space are operationally equivalent, and classical reality is understood as the record. In this scalar-clock / awareness-tensor / Trinity picture, an observation is any physical process that stabilizes correlations into durable, revisitable records, and gravity is interpreted as time decoherence: clock-locking and time selection into dominant mass time-zones. The paper introduces three phenomenological parameters that are exactly zero in standard GR+QM: (i) ϵ\epsilonϵ, the sensitivity of co-located clock rates to engineered decoherence and monitoring strength; (ii) η\etaη, the sensitivity of effective gravitational acceleration to record-export structure at fixed mass distribution; and (iii) a scalar time-mismatch scale ΔT∗\Delta T_\astΔT∗, beyond which interference visibility near a mass exhibits a protocol-dependent threshold. These parameters are tied to operational proxies: clock-locking depth, time mismatch, and coupling gradients. From this framework, three testable predictions follow: Entanglement-dependent time dilation: Two identical, co-located precision clocks in the same gravitational potential but in different record-coupling regimes (high vs. low monitoring and decoherence) should exhibit a small, persistent differential drift that tracks clock-locking depth, not altitude or velocity. Gravity modulation by engineered decoherence: In a torsion balance, atom interferometer, or precision gravimeter, the measured acceleration toward a test mass should differ slightly between “decoherence OFF” and “decoherence ON” conditions, even when the mass distribution and EM fields are unchanged. The key signature is a protocol-locked Δg\Delta gΔg that appears only when scattered quanta are recorded, not when the same fields are present but their outputs are dumped locally. Entanglement horizon near mass: In a matter-wave interferometer, as one arm approaches a mass (or as the mass is increased), interference visibility should drop at a characteristic threshold set by scalar-clock mismatch and record structure. This defines an “entanglement horizon” in time-mismatch space, distinct from smooth environmental decoherence. For each effect, the paper defines explicit null hypotheses, identifies leading systematics, and sketches minimal experimental protocols compatible with current or near-term optical clocks, gravimetry, and matter-wave interferometry platforms. A brief CPT-compatibility analysis clarifies that microscopic dynamics remain CPT-symmetric in the usual QFT sense; any asymmetries arise only at the coarse-grained level of record formation and clock-locking. The proposals can therefore be read either as parameterized extensions of GR+QM using measurement architecture as an additional knob, or as an operational test of a broader “gravity as time decoherence” interpretation in which geometry becomes explicitly record-sensitive. This Version 2 is a revised and expanded update of the original upload, adding a phenomenology-first summary, clarifying the roles of the parameters (ϵ,η,ΔT∗)(\epsilon,\eta,\Delta T_\ast)(ϵ,η,ΔT∗), and situating the framework more explicitly relative to existing work on gravity-related decoherence, hybrid classical–quantum gravity, and clock/interferometry proposals (Diósi–Penrose, Bassi, Anastopoulos–Hu, Oppenheim, Zych–Costa–Pikovski–Brukner, Bose et al.). The updated version explicitly restricts the criterion to record-sensitive effects, rather than any effect. It explicitly spells out what “record formation on/off” means in practice: detectors and logging are turned on/off while the physical fields are held fixed, i.e., outputs are either stored or not stored. This version tightens falsifiability and lab usability. It (i) commits to explicit benchmark model families for the three predictions, each reducing to standard physics when ϵ=η=κ=0\epsilon=\eta=\kappa=0ϵ=η=κ=0; (ii) defines an unambiguous export-axis variable via the exported mutual-information rate I˙XR\dot I_{XR}I˙XR and export depth E\mathcal{E}E, enabling cross-platform comparisons; (iii) adds a fully worked, platform-specific optical lattice clock pilot (C1 vs C2 export-only toggle) including invariance audits, confound/error budgeting, preregistered power/discriminability analysis, and an end-to-end analysis pipeline; and (iv) upgrades mandatory reporting/preregistration templates so null results produce publishable bounds on (ϵ,η,κ)(\epsilon,\eta,\kappa)(ϵ,η,κ).
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
Prevailing semi-classical models of quantum gravity treat gravitational fluctuations as a source of stochastic noise, predicting an inevitable degradation of quantum coherence (decoherence). Here, we present a counter-proposal derived from a ψ-epistemic extension of General Relativity. By introducing an effective quadratic tidal potential in a nonrelativistic EFT Hamiltonian, we show that vacuum (Weyl) curvature produces anisotropic squeezing—compression along the radial tidal eigen-direction and expansion transversely—which can increase detector overlap under appropriate mode matching, yielding an apparent narrowinga along the readout axis. This model predicts a constructive visibility shift (∆V > 0) in interferometric experiments, termed “Inverse Decoherence.” We propose the LENS experiment—a 87Rb trapped/guided atom interferometer (Deep Trap configuration) coupled to an oscillating 500 kg tungsten mass—to isolate this signature. Simulations indicate a signal magnitude of ∆V ≈ 1.26 × 10−6 with a signal-to-noise ratio of 10.7, distinguishable from gradient noise via k-vector reversal.
We give a first principles derivation of a master equation for the evolution of a quantum matter field in a linearly perturbed Minkowski spacetime, based solely on quantum field theory and general relativity. We make no additional assumptions nor introduce extra ingredients, as is often done in alternative quantum theories. When the quantum matter field is projected to a one-particle state, the master equation for a non-relativistic quantum particle in a weak gravitational field predicts decoherence in the energy basis , in contrast to most existing theories of gravitational decoherence. We point out the gauge nature of time and space reparameterizations in matter–gravity couplings, and warn that 'intrinsic' decoherence or alternative quantum theories invoking stochastic dynamics arising from temporal or spatial fluctuations violate this fundamental symmetry of classical general relativity. Interestingly we find that the decoherence rate depends on extra parameters other than the Planck scale, an important feature of gravitational decoherence. This is similar to the dependence of the decoherence rate of a quantum Brownian particle to the temperature and spectral density of the environment it interacts with. The corresponding features when gravity acts as an environment in decohering quantum objects are what we call the ' textures' of spacetime . We point out the marked difference between the case when gravity is represented as a background spacetime versus the case when gravity acts like a thermodynamic bath to quantum particles. This points to the possibility of using gravitational decoherence measurements to discern whether gravity is intrinsically elemental or emergent.
This thesis investigates the role of gravitational waves in quantum systems, motivated by advances in our understanding of the quantum–gravity interface and efforts to identify experimental signatures of quantum gravity. It focuses on gravitational decoherence and the interplay between internal energy and centre-of-mass dynamics in composite quantum systems, complemented by a study of internal-energy effects in gravitationally mediated entanglement. First, we develop relativistic Hamiltonian formulations showing that changes in a composite system’s internal energy increase its gravitational mass rather than alter its momentum. This removes earlier ad hoc arguments for eliminating “anomalous friction forces”. We show that gravitational waves act as a dynamical background, inducing curvature-dependent forces that modify total momentum. Second, we revisit a thought experiment in which tensions between causality and complementarity arise. We identify a scenario in which these tensions follow from energy–mass equivalence, making the effect specific to gravitational interactions. In a gravitationally mediated entanglement experiment using Newtonian gravity as mediator, we investigate whether decohering gravitational radiation can resolve the apparent conflict. Finally, we build upon a model of gravitational decoherence consistent with general relativity. This requires deriving a higher-derivative quantum Langevin equation and master equation. The resulting dynamics show that gravitational interactions induce decoherence in the canonical momentum basis of the quadrupole and generate acceleration- and jerk-dependent corrections absent in electrodynamics. Together, these results show that weak-field gravitational interactions leave distinct relativistic imprints on quantum systems, including effects unique to gravitational waves, providing potential signatures that distinguish gravity from other interactions.