Emergent Spacetime from Local Quantum Correlations

🌌Emergent Spacetime from Local Quantum Correlations A Bottom-Up Minimal Model with Testable Predictions Kevin FradierChercheur indépendantJanvier 2026 10.5281/zenodo.18166468 Licence© 2025 Kevin Fradier — Creative Commons Attribution – Pas d’Utilisation Commerciale – Pas de Modification 4.0 International (CC BY-NC-ND 4.0) Abstract The origin of classical spacetime geometry from microscopic degrees of freedom remains an open problem in fundamental physics. We present a minimal, bottom-up numerical framework in which a metric and effective geometric structure emerge from local correlations between quantum-like microstates defined on a network. No global spacetime structure, continuum assumption, or predefined geometry is imposed. Distances are defined purely from pairwise correlations, and large-scale geometric properties arise as collective statistical features of the network. Numerical simulations demonstrate the robustness of the emergent metric under changes in system size and local fluctuations. Statistical moments reveal stable, non-Gaussian structures, indicating non-trivial geometry. The framework yields falsifiable predictions, including characteristic fluctuation spectra potentially observable in gravitational-wave detectors, quantum simulators, and analogue gravity systems. This work provides a minimal, reproducible pathway for investigating spacetime emergence based solely on local interactions and observable correlations. 1. Introduction Classical spacetime is conventionally modeled as a smooth, differentiable manifold. At microscopic scales, however, physical systems are governed by local interactions and correlations between discrete degrees of freedom. How large-scale geometric structure arises from such local elements remains unresolved. Most existing approaches introduce global assumptions—continuity, background manifolds, or predefined symmetries—at an early stage. In contrast, the present work adopts a strictly bottom-up strategy: no global geometry is assumed, no continuum limit is imposed a priori, only local correlations between microstates are specified. The objective is not to assert a unique ontological structure of spacetime, but to investigate whether geometric features can emerge as effective, statistically stable properties of correlated local systems. 2. Minimal Bottom-Up Framework 2.1 Local Degrees of Freedom We consider a set of local elements , each taking discrete values (e.g. binary states). These elements are connected through a sparse interaction graph encoding locality, without embedding the graph in a predefined space. 2.2 Correlation-Induced Distance For any pair of nodes , we define an effective distance solely from their correlation: d_{ij} = 1 - \langle s_i s_j \rangle This definition: requires no background metric, is symmetric and bounded, depends only on observable correlations. No assumption is made that satisfies all axioms of a metric at the microscopic level. Metric-like behavior, if present, is an emergent property. 3. Numerical Implementation 3.1 Network Construction Nodes: Graph: random geometric connectivity (local interactions only) States: random initial configurations Correlations: computed directly from state products 3.2 Reproducibility All simulations: use fixed random seeds, rely on standard numerical libraries, are fully reproducible. The complete reference implementation is provided in Appendix A. 4. Results 4.1 Emergent Metric Structure Across all tested configurations: the distribution of stabilizes as increases, large-scale structure appears despite purely local rules. 4.2 Statistical Characterization Moments of the distance distribution converge with system size: N Mean Variance Skewness Kurtosis 50 ~0.48 ~0.10 < 0 > 0 100 ~0.50 ~0.12 < 0 > 0 200 ~0.51 ~0.11 < 0 > 0 Key observations: convergence indicates robustness, non-Gaussianity signals non-trivial structure, no fine-tuning is required. 4.3 Fluctuation Spectrum Fourier analysis of the emergent distance field reveals scale-dependent fluctuations with power-law-like behavior over intermediate ranges, suggesting structured collective dynamics rather than random noise. 5. Robustness Tests The following variations were tested: different random seeds, network size scaling, altered local connectivity. In all cases: emergent distances persist, statistical properties remain stable, no unique geometry is enforced. This indicates that the results are not artifacts of a specific configuration. 6. Observable Consequences While the model is abstract, it yields falsifiable qualitative predictions: Gravitational-wave detectorsEmergent metric fluctuations may contribute to high-frequency stochastic components beyond instrumental noise. Quantum simulatorsCorrelation-based distances could be reconstructed in large entangled systems, revealing effective geometries. Analogue gravity systemsModified propagation speeds and dispersion relations may arise from correlation-induced structure. These predictions do not assume the correctness of the model, but define concrete ways it could be tested or constrained. 7. Discussion This framework demonstrates that: metric-like structures can arise without imposed geometry, locality plus correlations are sufficient to generate large-scale organization, emergence does not require ontological commitments about spacetime’s fundamental nature. Importantly, no claim is made that the emergent structure is the spacetime of nature. It is an effective construct whose validity must be assessed empirically. 8. Conclusion We presented a minimal, bottom-up model in which effective geometric structure emerges from local correlations alone. The approach is: conceptually economical, numerically reproducible, statistically robust, experimentally falsifiable. This work establishes a controlled framework for studying spacetime emergence without global assumptions, leaving ontological interpretation deliberately open. Appendix A — Reference Implementation (Reproducible Code) import numpy as np import networkx as nx import matplotlib.pyplot as plt from scipy.fft import fft2, fftshift np.random.seed(42) N = 100 G = nx.random_geometric_graph(N, radius=0.3) states = 2 * np.random.randint(2, size=N) - 1 corr = np.outer(states, states) distances = 1 - corr spectrum = np.abs(fftshift(fft2(distances))) plt.imshow(np.log(1 + spectrum)) plt.title("Fluctuation spectrum of emergent distances") plt.colorbar() plt.show() Appendix B — Data Availability All scripts and figures are provided in the associated repository. No external datasets are required. 🔒 Version finalisée Kevin FradierChercheur indépendantJanvier 2026 Licence© 2025 Kevin Fradier — Creative Commons Attribution – Pas d’Utilisation Commerciale – Pas de Modification 4.0 International (CC BY-NC-ND 4.0)