Microscopic Stress–Energy Correlations and Emergent Stochasticity A Matter-Side Framework Within Standard General Relativity

The fundamental equations governing known matter and fields are deterministic, yet their observable microscopic behavior is intrinsically probabilistic. Radioactive decay, scattering events, and noise phenomena are described statistically, even when the underlying dynamics contain no stochastic terms. The origin of this apparent randomness remains a foundational question. In this work, we develop a conservative, matter-side framework in which micro- scopic stochasticity emerges from the structural properties of the stress–energy tensor within standard general relativity. Treating stress–energy as a composite operator and consistently coarse-graining it over finite spacetime regions, we show that long-range, charge-mediated correlations can survive averaging and contribute irreducible variance to effective gravitational sourcing. When such extended correlations are disrupted or suppressed, probabilistic behavior arises naturally despite deterministic microscopic dynamics. The framework introduces a clear separation between confined stress–energy, which fixes intrinsic energy scales, and extended stress–energy correlations, which govern variance, decay statistics, and noise. Stochasticity is therefore interpreted as a struc- tural consequence of correlation loss rather than as a fundamental indeterminism or an added dynamical ingredient. All standard symmetries, conservation laws, and local tests of general relativity are preserved. The result is a unified, falsifiable account of decay, fluctuations, and irreversibility as emergent features of organized matter, without modifying quantum field theory or Einstein’s equations.