Overview
The middle paper in the three-part LQG internal-time sequence. It takes the internal-time functional established in the bounce paper and uses it to verify — numerically, to machine precision — that classical General Relativity emerges from LQG at macroscopic scales.
What the paper shows
Five headline results from seven numerical experiments:
- Einstein-equation emergence verified to ε < 10⁻¹⁶ machine precision in vacuum, with < 0.001% consistency error between area and scale factor.
- Gauge invariance — volume and entropy clock choices yield perfectly correlated geometries (ρ = 1.000), confirming clock choice as pure gauge.
- Matter emergence — radiation-dominated scaling emerges naturally with only a 1.58% deviation from the theoretical H ∝ a⁻², suggestive of an intrinsic quantum-geometry feature.
- Singularity resolution — confirms the bounce paper's finding, a_min = 0.707 ℓ_P.
- Scalability — T_comp ∝ N^1.66 up to N = 600.
Where it sits
Continuation of the bounce paper and direct precursor to the scalable simulations paper.