GRUT Gravitational Decoherence from the CTP Influence Functional: A Zero-Parameter Prediction with Six Discriminating Signatures
D. Ryan Grover
GRUT Gravitational Decoherence from the CTP Influence Functional: A Zero-Parameter Prediction with Six Discriminating Signatures We derive the gravitational decoherence rate for mesoscopic objects from the imaginary part of the Schwinger-Keldysh (closed-time-path) influence functional. The derivation requires no assumptions beyond the CTP axioms — path doubling and retarded variation — and the Newtonian limit of the graviton propagator. No coupling constants, collapse rates, or correlation lengths are introduced. The decoherence rate Λ_grav = Gm²S(l/R)/(ℏl), with the extended-body suppression factor S(l/R) = min(1, (l/R)³/6), is a direct output of the imaginary part of the CTP influence functional, following the approach of Anastopoulos and Hu (2013). The paper is self-contained: it derives the decoherence rate from the CTP influence functional alone, without reference to the broader GRUT constitutive framework. The prediction produces six experimentally discriminating signatures that collectively fingerprint gravitational decoherence: mass-squared scaling (F1), geometry dependence through S(l/R) distinguishing gold from silica at the same mass (F2), a pressure-independent decoherence plateau as environmental noise is removed (F3), far-field separation scaling Λ ~ l⁻¹ (F4), entanglement protection where Bell states decohere slower than product states (F5), and a geometric kink at l = 6¹/³R ≈ 1.817R where the near-field l² regime transitions to the far-field 1/l regime (F6). An adversarial comparison against five competing models — constant floor, power-law, CSL, Diósi-Penrose point-mass, and Penrose objective reduction — shows that no tested alternative reproduces all six signatures simultaneously. The geometric kink (F6) kills all point-mass models, geometry dependence (F2) kills all constant-floor models, and entanglement protection (F5) kills all state-independent models. A single experiment measuring F1 + F2 + F6 would be decisive. All experimental benchmarks use realizable objects with known material densities — correcting previous literature benchmarks that assumed physically inconsistent parameters. The gold microsphere benchmark (R = 1 μm, m = 80.8 pg, l = 1 μm) produces Λ_grav ~ 689 Hz with coherence time ~1.5 ms. A silica sphere at the same mass demonstrates the geometry signature (F2) with a different rate. Heating from gravitational momentum diffusion is safe by more than 60 orders of magnitude — the extended-body suppression S(l/R) prevents the UV divergence that causes heating problems in point-mass models. The prediction is robust against non-Markovian corrections because it depends on the noise kernel (a property of the quantum state and the gravitational field), not on the dynamical evolution equation. Theoretical corrections to the kernel — post-Newtonian O(10⁻¹⁶), 2-loop graviton O(10⁻⁸), compactness O(10⁻²⁷) — are negligible at laboratory scales. A concrete experimental proposal targets next-generation optomechanical systems at the 10-picogram scale. The required parameters (mass > 10 pg, separation > 100 nm, pressure < 10⁻¹⁰ Pa, temperature < 100 mK, coherence time > 1 ms) are within reach of current technology trajectories. Four target experimental groups are identified: Arndt (Vienna), Aspelmeyer (Vienna), Geraci (Northwestern), and Bateman (UCL). The protocol specifies six steps from superposition preparation through pressure scanning, material comparison, and kink identification. If the decoherence rate continues to decrease with pressure below 10⁻¹⁰ Pa (no plateau), the prediction is falsified. Through the decoherence-cosmology bridge, a single laboratory measurement of Λ_grav at any (m, l) would fix τ₀ independently and determine the vacuum expansion rate of the universe — connecting a tabletop measurement to the cosmological constant. Key Insights: 1. Gravitational decoherence rate Λ_grav = Gm²S(l/R)/(ℏl) derived from the CTP influence functional with zero free parameters — self-contained, no reference to the broader GRUT framework required 2. Six experimentally discriminating signatures (F1–F6) that no tested alternative decoherence model reproduces simultaneously 3. The geometric kink at l = 6¹/³R ≈ 1.817R is the single most discriminating feature — it kills all point-mass models and requires only measuring Λ(l) across the near-field/far-field transition 4. A single experiment measuring F1 (mass-squared) + F2 (geometry) + F6 (kink) would be decisive, even without reaching the absolute rate 5. Corrected benchmarks using realizable objects: gold microsphere (R = 1 μm, m = 80.8 pg) produces Λ ~ 689 Hz — previous literature benchmarks at 10 pg / R = 50 nm are physically inconsistent 6. Heating from gravitational momentum diffusion is safe by > 60 orders of magnitude — extended-body suppression prevents the UV divergence of point-mass models 7. Robust against non-Markovian corrections: the rate depends on the noise kernel (pre-dynamical), not the equation of motion 8. Theoretical corrections negligible at lab scales: post-Newtonian O(10⁻¹⁶), 2-loop graviton O(10⁻⁸), compactness O(10⁻²⁷) 9. Concrete experimental proposal for optomechanical systems at 10 pg scale, with required parameters, six-step protocol, and explicit positive/null result criteria 10. Four target experimental groups identified: Arndt, Aspelmeyer, Geraci, Bateman 11. Adversarial comparison: five competing models tested, each killed by complementary signature failures — no single alternative survives the full six-signature space 12. Decoherence-cosmology bridge: a single lab measurement of Λ_grav fixes τ₀ and determines the vacuum expansion rate — connecting a tabletop experiment to the cosmological constant
•Apr 18, 2026•0 citations