Time Is Not Fundamental: The Einstein-GSL Completion of General Relativity

For over three centuries, physics has treated time as a fundamental primitive: a continuous parameter flowing independently of physical processes. This assumption persists from Newton through Einstein to modern quantum mechanics, leaving core mysteries unresolved: Why does time flow? Why does it possess an arrow? Why does it dilate? We demonstrate that time cannot be fundamental. By elevating the Generalized Second Law (GSL), information discreteness, and quantum uncertainty to axiomatic status, we treat irreversible change—not duration—as primitive. We introduce Discrete Entropy Updates (DEUs) as irreducible quanta of change and derive proper time non-circularly as: dτ = (ℏ / ⟨E⟩) dλ where λ counts DEUs. This relation does not assume pre-existing time; it defines time from atemporal principles. It immediately explains time dilation as variations in local entropy-update rates and the arrow of time as the GSL inequality. As a strong consistency check, our framework independently recovers the Connes-Rovelli thermal time hypothesis. We extend General Relativity to non-equilibrium conditions via the Einstein-GSL Completion, showing how Einstein’s field equations emerge as the reversible, zero-entropy-production limit of a more general entropy balance law. This framework synthesizes thermodynamics, information theory, and gravity into a coherent picture where entropy—not time—is fundamental.