Quantum Gravity and String Theory

Statistical Emergence of Lorentz Symmetry in Stochastic Nonlocal Causal Networks

Authors: Hamza Akyüz

This study investigates the statistical emergence of Lorentz symmetry within stochastic, nonlocal causal networks. By employing a Poisson sprinkling process to construct discrete spacetime configurations, we analyze the micro-local fluctuations of causal connections. Using a specialized numerical simulation in Python, we evaluate the distribution of invariant spacetime intervals and perform a Kolmogorov-Smirnov test to quantify the convergence toward continuous Lorentz invariance. Our results demonstrate that while discrete nonlocality introduces deviations at the Planck scale, classical Lorentz symmetry emerges macroscopically as a statistical steady-state property of the network ensemble.

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[v1] 2026-05-18 12:17:22

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