Discrete Directed Temporality: A Foundational Axiom for Physics

This essay proposes that the arrow of time — the intrinsic directionality and discreteness of temporal evolution — should be treated as a foundational axiom of physics rather than a phenomenon to be derived from other principles. The argument proceeds in stages: (1) entropy increase is identified as a statistical symptom rather than a fundamental law; (2) causality is shown to presuppose temporal directionality, making directionality logically prior; (3) temporal directionality is argued to function as a Gödelian presupposition of physical formalism — necessary for the system to operate but inexpressible within it; (4) the historical analogy with the ultraviolet catastrophe motivates the addition of discreteness to directionality; (5) the combined axiom of Discrete Directed Temporality (DDT) is argued to dissolve the quantum measurement problem, resolve spacetime singularities, address the cosmological constant discrepancy, force spatial discreteness through Lorentz covariance, and provide a natural framework for unifying quantum mechanics and general relativity. The essay positions DDT relative to existing programs (causal set theory, causal dynamical triangulations, loop quantum gravity, GRW collapse models) and identifies testable predictions that distinguish it from standard physics.