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Gravitationally Induced Entanglement Between Two Masses: A Registered Prediction of No Witness Below an Entangling Phase of 2 Rad, At Any Constant Recording Rate

David Swanson

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.2139/ssrn.7617198

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Gravitationally induced entanglement between two masses: a registered prediction of no witness below an entangling phase of 2 rad, at any constant recording rate

David Swanson

I register the prediction that no experiment will witness gravitationally induced entanglement between two masses, each in two branches, while their entangling phase stays below 2 rad, at any constant rate at which each mass's environment records its position. Under gravity whose source in each description is a function of the system's reduced state, conditioned on every record that exists, two masses that nothing records stay in a product state at every entangling phase. Recorded masses stay unentangled while the phase is below 4 rad with each mass's share counted once, or below 2 rad with each mass taking its full potential. Every published parameter set computed here lies below both, between 0.0150 rad and 0.594 rad. A witness of gravitationally induced entanglement reported at 5 standard deviations in any such experiment excludes the prediction on its own, whatever the recording rate. Quantized gravity entangles the masses only while each is recorded more slowly than a threshold set by the experiment's parameters, 0.0623 /s at Bose et al.'s, so a null result counts against it only where an experiment establishes its recording rate below that threshold. The source in the description occupying branch A is n_r^A = n_A + f(η) (n_B − n_A)/2, where n_A and n_B are the branches' densities and η is the overlap of the mass's two branch records, e^(−Γ t) at recording rate Γ. The product state is derived; the weight f(η) = η is derived from the stated condition that the source depend affinely on the coherence; the phase bound is computed in a two-branch open-system model and rests on the stated two-body form. Nothing is fitted. The statistic is the reported witness with the recording rate the experiment establishes, read against both predictions at its own parameters; the chance of a false exclusion from statistical fluctuation alone is 2.9 × 10⁻⁷ for each experiment.

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Gravity can both generate quantum entanglement and cause decoherence through time-dilation effects. This note studies the competition between these two effects by treating them as consequences of the same Newtonian mass–energy interaction. Using a solvable two-body model with a coupling between energy and geometry, the work shows that the position-dependent part of the interaction produces the entangling phases associated with gravitationally induced entanglement, while the energy-dependent part produces proper-time decoherence. The paper computes this race exactly and derives several results. First, the outcome is independent of the strength of gravity itself: the dynamics depends only on the combination of coupling strength and interaction time, meaning that gravity sets the timescale but does not determine the final verdict. The result is controlled by the structure of the interaction and the geometry of the quantum state. Second, a registered prediction that internal energy spread would eventually destroy gravitational entanglement is disproved by the exact calculation. Instead, the entanglement decreases but approaches a nonzero geometry-dependent floor. The mechanism is traced to the energy-product coupling, which produces a non-Gaussian characteristic function and prevents complete suppression of the entangling effect. Third, the work derives an exact separability boundary: two sources with spatial coherences v1 and v2 become entangled at the optimal phase precisely when (1 + v1)(1 + v2) > 2. Fully decohered sources cannot generate entanglement, while partial coherence can be sufficient. Finally, the paper verifies that the record–decoherence relation holds inside the same gravitational interaction: coherence lost by a system equals the information recorded by the rest of the universe, combining entanglement and proper-time decoherence into a single information budget. The results are obtained within finite exactly solvable models with declared limitations: static branches, Newtonian-form coupling, no graviton exchange, and no dynamical quantum gravity. The work provides a controlled theoretical framework for understanding the competition between gravitationally induced entanglement and gravitational decoherence.

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Parameter Scanning in a Quantum-Gravity-Induced Entanglement of Masses

Martine Schut, Anupam Mazumdar

•Jan 1, 2025•1 citation
I register the prediction that no experiment will witness gravitationally induced entanglement between two masses, each in two branches, while their entangling phase stays below 2 rad, at any constant rate at which each mass's environment records its position. Under gravity whose source in each description is a function of the system's reduced state, conditioned on every record that exists, two masses that nothing records stay in a product state at every entangling phase. Recorded masses stay unentangled while the phase is below 4 rad with each mass's share counted once, or below 2 rad with each mass taking its full potential. Every published parameter set computed here lies below both, between 0.0150 rad and 0.594 rad. A witness of gravitationally induced entanglement reported at 5 standard deviations in any such experiment excludes the prediction on its own, whatever the recording rate. Quantized gravity entangles the masses only while each is recorded more slowly than a threshold set by the experiment's parameters, 0.0623 /s at Bose et al.'s, so a null result counts against it only where an experiment establishes its recording rate below that threshold. The source in the description occupying branch A is n_r^A = n_A + f(η) (n_B − n_A)/2, where n_A and n_B are the branches' densities and η is the overlap of the mass's two branch records, e^(−Γ t) at recording rate Γ. The product state is derived; the weight f(η) = η is derived from the stated condition that the source depend affinely on the coherence; the phase bound is computed in a two-branch open-system model and rests on the stated two-body form. Nothing is fitted. The statistic is the reported witness with the recording rate the experiment establishes, read against both predictions at its own parameters; the chance of a false exclusion from statistical fluctuation alone is 2.9 × 10⁻⁷ for each experiment.
Gravity can both generate quantum entanglement and cause decoherence through time-dilation effects. This note studies the competition between these two effects by treating them as consequences of the same Newtonian mass–energy interaction. Using a solvable two-body model with a coupling between energy and geometry, the work shows that the position-dependent part of the interaction produces the entangling phases associated with gravitationally induced entanglement, while the energy-dependent part produces proper-time decoherence. The paper computes this race exactly and derives several results. First, the outcome is independent of the strength of gravity itself: the dynamics depends only on the combination of coupling strength and interaction time, meaning that gravity sets the timescale but does not determine the final verdict. The result is controlled by the structure of the interaction and the geometry of the quantum state. Second, a registered prediction that internal energy spread would eventually destroy gravitational entanglement is disproved by the exact calculation. Instead, the entanglement decreases but approaches a nonzero geometry-dependent floor. The mechanism is traced to the energy-product coupling, which produces a non-Gaussian characteristic function and prevents complete suppression of the entangling effect. Third, the work derives an exact separability boundary: two sources with spatial coherences v1 and v2 become entangled at the optimal phase precisely when (1 + v1)(1 + v2) > 2. Fully decohered sources cannot generate entanglement, while partial coherence can be sufficient. Finally, the paper verifies that the record–decoherence relation holds inside the same gravitational interaction: coherence lost by a system equals the information recorded by the rest of the universe, combining entanglement and proper-time decoherence into a single information budget. The results are obtained within finite exactly solvable models with declared limitations: static branches, Newtonian-form coupling, no graviton exchange, and no dynamical quantum gravity. The work provides a controlled theoretical framework for understanding the competition between gravitationally induced entanglement and gravitational decoherence.