Emergent Tensor Gravity
Derivation of the TT sector from Lindblad dynamics. Shows how gravitational waves emerge from quantum decoherence.
Key: Jump operators couple to stress-energy quadrupole
From Quantum Decoherence to Spacetime Geometry
A Multi-Agent Cognitive Architecture Exploration
"Gravity is not fundamental. It emerges from quantum mechanics through the irreversible process of decoherence."
This research program explores a radical hypothesis: Einstein's field equations arise naturally when quantum systems decohere through interaction with vacuum fluctuations. The transverse-traceless (TT) sector of gravitational perturbations — the only physical, propagating degrees of freedom — emerges from Lindblad dynamics.
Lorentz invariance emerges as an IR attractor — selected, not assumed
Where geometry matters: spheres don't couple to vacuum fluctuations (monopole = 0), but elongated objects like rods and needles have strong quadrupole coupling.
Open quantum systems evolve via the Lindblad master equation. The jump operators encode how the environment "measures" the system.
Only transverse-traceless modes carry physical gravitational information. Constraint modes (scalar, vector) are gauge artifacts that don't propagate.
The multipole moment Qℓ determines coupling strength. Shape encodes how strongly an object "feels" vacuum fluctuations.
A key result: the characteristic frequency is set by the light-crossing time of the object:
This emerges naturally from the bath spectral density — the only dimensionally consistent choice without fine-tuning.
Lorentz invariance is not put in by hand — it emerges as an IR attractor under RG flow.
βLV < 0 → Lorentz violation flows to zero in IR
Time and space are both emergent from a deeper structure — causal order encoded in process tensors.
"Who can affect whom" → spacetime geometry
14 documents generated through CAWM tree search, exploring emergent gravity from multiple angles.
Derivation of the TT sector from Lindblad dynamics. Shows how gravitational waves emerge from quantum decoherence.
Ward identities ensure the emergent theory satisfies diffeomorphism invariance — Einstein's equations arise automatically.
Explicit derivation of how the vacuum "measures" matter configurations via TT gravitational modes.
Counterexample analysis: can gravity emerge differently? Explores uniqueness of the Lindblad route.
Theorem proving Lorentz symmetry of emergent gravity follows from microscopic constraints.
Detailed mechanism: how relativistic invariance emerges from non-relativistic quantum mechanics.
How causal order emerges from timeless quantum mechanics through decoherence.
Newton's constant G is computed from bath parameters: G = 4π/λ²N². Heating and drag vanish by Lorentz symmetry.
Two-level dictionary showing how background-free quantum gravity maps to emergent spacetime.
Sphere vs dumbbell test: spheres (monopole) don't decohere gravitationally. Quantum correlations can be negative — impossible for classical noise.
EFT deformation analysis: how stable is the framework under perturbations?
Rate formula derivation with correct dimensional analysis: ω₀ = c/R emerges uniquely.
Adversarial analysis of the framework. Stress-testing assumptions and identifying weak points.
Rigorous proof that direct vacuum coupling alone is insufficient. This finding motivated the search for Framework C.
A rigorous proof that direct quantum vacuum coupling is too weak — motivating the search for Framework C.
For any biological system at temperature T ≥ 273 K:
No amplification mechanism consistent with the TT framework can close this gap.
| Object | Mass (kg) | (M/MP)² |
|---|---|---|
| Mesoscopic probe | 10⁻⁴ | 2 × 10⁻⁸ |
| Biological cell | 10⁻¹² | 2 × 10⁻²⁴ |
| Protein complex | 10⁻²² | 2 × 10⁻⁴⁴ |
| Object | Size R | ω₀ (Hz) |
|---|---|---|
| Mesoscopic probe | 0.3 mm | 10¹² |
| Cell | 10 μm | 3 × 10¹³ |
| Protein | 10 nm | 3 × 10¹⁶ |
Qℓ² ≤ 1 for any shape. Geometry alone cannot close the gap.
NoN² scaling needs 10⁸ coherent elements — impractical at room temperature.
NoQ-factors ~10 in warm systems. Thermal broadening kills enhancement.
NoCognitive Agent with World Model — the multi-agent tree search system that generated these findings.
Each agent proposes 3 solution branches based on their expertise
All agents score branches; highest-voted branch is selected
Critical review may trigger backtrack for breadth exploration
Repeat until target score (10.0) reached or depth limit