Time, Space, and Bell's Inequality: An Informational Route to Emergent Spacetime

This work explores the idea that space and time are not fundamental backdrops but emergent phenomena arising from quantum information. Building on the Horizon Information Framework, the article proposes that time appears as an informational rhythm, while space arises from entanglement correlations between horizon degrees of freedom. A central claim is that the existence of space is inseparable from the violation of Bell’s inequality. Classical correlations fail to sustain spatial extension, whereas quantum correlations generate the connectivity network perceived as geometry. This principle is refined into an operational criterion: space exists only when Bell’s inequality is violated and the entanglement network has nonzero effective dimensionality with sufficient correlation length. The framework is falsifiable: any mismatch between Bell correlations, effective dimension, and critical scaling would refute it. Consequences include new interpretations of cosmological tensions, vacuum energy scaling, black hole evaporation, and dimensional flow in the early universe. Laboratory Bell tests, spectral-dimension probes, and cosmological observations are discussed as possible avenues for testing the proposal. In summary, the article places Bell’s inequality at the heart of fundamental physics, recasting it from a test of hidden variables into an operational principle for the very existence of spacetime. This work consolidates several companion studies into a coherent Horizon Information Framework, aiming to provide a falsifiable and information-based foundation for cosmology and quantum gravity. Further resources and related publications are available through the Horizon Information Framework community on Zenodo.