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Jaehong Oh

χPreprint · 2025

Scalable Loop Quantum Gravity Simulations with Information-Geometry Mixed Potential

Jaehong Oh

134 words1 min read

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Abstract

We present a scalable computational framework for Loop Quantum Gravity (LQG) simulations based on a novel information-geometry mixed potential that implements a smooth quantum-to-classical transition. Building on our previous internal-time functional T[γ] defined on spin-network configuration space, we introduce a dynamically weighted potential Φ_IG(a) = α(a)S + β(a)⟨V̂⟩, where entropy S dominates at small scales (quantum regime) and volume ⟨V̂⟩ dominates at large scales (classical regime). Through systematic scaling experiments on spin networks from N = 2 to N = 100 nodes across three graph topologies (cubic lattice, random, scale-free), we establish four key results: (1) universal internal-time convergence T_total ≈ 5–6 independent of system size for N ≳ 25; (2) sub-quadratic computational scaling T_comp ∝ M^{1.74}; (3) robust singularity resolution (13/15 simulations show bounce with a_min > 0); (4) validation consistent with prior N = 2 work within 10%.

Overview

Third in a sequence on LQG with explicit internal time. This paper tackles the scalability question: can the framework, previously validated on 2-node toy models, run on networks of ~100 nodes while preserving physical validity?

What the paper shows

  • Universal internal-time convergence — a crossover at N ≈ 25 beyond which total internal time T_total saturates near ≈ 5–6, a genuinely system-size-independent timescale for quantum cosmological bounces.
  • Sub-quadratic scaling — algorithm complexity T_comp ∝ M^1.74 (with M edges), tractable on standard workstations.
  • Singularity resolution robustness across random, cubic-lattice, and scale-free topologies.
  • Delivered with ~7,850 lines of open-source implementation.

Where it sits

Companion paper to the two earlier LQG manuscripts on quantum bounce and internal-time GR emergence. Together they form the foundation for the absolute-time and mathematical-foundations strand of the notes.

BibTeX· generated

@misc{oh2025lqg,
  title   = {Scalable Loop Quantum Gravity Simulations with Information-Geometry Mixed Potential},
  author  = {Jaehong Oh},
  year    = {2025},
  url     = {https://jack0682.github.io/papers/lqg-scalable-info-geometry/},
}