When the Clock Stutters: A Theoretical Extension of Time Dilation Under Acceleration

This paper presents a theoretical extension to special relativity by introducing acceleration-dependent modifications to time dilation. The Clock Hypothesis—an assumption that acceleration has no effect on the ticking of a clock—is upheld by all known experimental data but remains an unproven postulate. Here, we explore whether acceleration might play a role under extreme conditions by introducing a perturbation function ε(a)ε(a) to the Lorentz factor.We propose and compare three candidate models—quadratic, exponential, and logarithmic—to assess their mathematical behavior and physical plausibility. Using 2D and 3D simulations, we visualize their effects across a range of velocities and accelerations, identifying failure boundaries where classical assumptions may break down. Among the models, the exponential form demonstrates bounded, stable behavior consistent with saturation effects observed in other physical systems.This framework does not contradict special relativity, but invites deeper inquiry into its limits—particularly near regimes involving extreme acceleration, time saturation, and quantum gravity. We present this work as a tool for theoretical exploration and interdisciplinary modeling, with implications for relativistic physics, AI cognition under acceleration, and the philosophy of time.