Sequential Minimum-Length Structure Consistent with the Constant Speed of Light

Sequential Minimum-Length Structure Consistent with the Constant Speed of Light This paper examines how a discrete, minimum‑length structure of spacetime can remain fully consistent with the observed constancy of the speed of light. Building on earlier work showing that a finite minimum length arises inevitably from the consistency of quantum localization, gravitational collapse, and causal structure, this study focuses on the dynamical implications of such a minimum length. If physical states evolve through discrete updates separated by the minimum length, then change does not occur through infinitesimal continuous variations but through sequential transitions along an ordered structure. This paper analyzes the rate of these updates and demonstrates that, when the update rate is constant, the effective propagation speed along the discrete sequence becomes constant as well. Under this condition, the propagation speed naturally matches the observed invariant speed of light. Importantly, this framework does not modify or reinterpret the postulates of special relativity. Instead, it shows that a discrete minimum‑length structure can reproduce the constant speed of light without conflicting with Lorentz symmetry. The analysis aligns with known results in quantum gravity research, where discrete structures can remain compatible with relativistic invariance. The results suggest that the constancy of the speed of light may reflect a deeper property of the sequential update process inherent to a minimum‑length spacetime. This provides a conservative and coherent perspective in which discrete spacetime structure and special relativity coexist without contradiction.