A_Reconsidering Causal Structure from a Distributional Time Direction

This paper introduces a minimal reinterpretation of the time direction by treating it as a distribution rather than a single one‑dimensional axis. Without adding any new physical assumptions, the approach focuses solely on the support structure of the distribution and shows that clear causal boundaries naturally emerge from it. The resulting causal structure is fully consistent with that assumed in special relativity, while providing an upstream geometric perspective on why causal boundaries arise in the first place.

The framework does not modify existing physical theories. Instead, it offers a supplemental viewpoint on the origin of causality by relaxing the conventional assumption that the time axis is uniquely defined and strictly one‑dimensional. The distributional description captures the asymmetry between the past (convergent and fixed) and the future (extended and uncertain), and explains how the outer edge of the distribution’s support yields a causal boundary aligned with the light cone.

This work serves as the conceptual foundation for a broader research program in which gravity, quantum behavior, and internal degrees of freedom are interpreted as geometric features of the future‑direction distribution. The present paper focuses on the minimal structure required for causal boundaries to emerge and establishes compatibility with existing relativistic frameworks.