Omega Theory Extended Preprint

The Wheeler–DeWitt equation H |Ψ⟩ = 0 describes a timeless quantum state of the universe, raising the problem of time: how do classical dynamics and the thermodynamic arrow emerge from an atemporal constraint? Omega Theory proposes a minimal framework with four classical compatibility rules as relational selection conditions on the superspace. These rules—local conservation of classical observables, strictly non-decreasing global entropy, minimum difference between compatible configurations, and diagonal correlation preserving continuity—directly derive the emergence of stable classical traces, local conservation laws, the irreversible thermodynamic arrow, monotonic mutual information growth, and continuity of classical trajectories. The process is eternal and asymptotic: mutual information approaches a maximum without attainment in finite time, ensuring persistent temporal dynamics. The theory extends naturally to higher levels of organization once recursion emerges as a stable negative-feedback loop in complex matter. This leads to the first self-replicating molecule, multilevel organization up to subjective consciousness (qualia as private classical traces), biological evolution, multicellular super-traces, cooperative societies, and the directional historical trend toward greater collective mutual information. The formulation distinguishes strict physical derivations from probable emergent consequences, offering a unified framework from quantum gravity to consciousness and history without additional fundamental principles.