A Physical Resolution of Zeno's Paradox through Consideration of Planck Length and Planck Time

Abstract This work examines Zeno’s paradox of Achilles and the tortoise while taking into account the physical limits of space and time. Although the paradox relies on the assumption of infinite divisibility, modern physical concepts such as Planck length and Planck time show that notions like “distance,” “position,” or “instant” lose operationally definable meaning below certain scales. Based on classical kinematics, it is shown that Achilles catches up with the tortoise once the remaining distance falls below the Planck length and therefore becomes physically unmeasurable. The infinite sequence of subdivisions required by Zeno’s argument loses its significance below this scale. The results demonstrate that the paradox arises solely from the assumption of infinite divisibility and disappears under realistic physical conditions. Modern physics thus provides a consistent and conceptually clear resolution of the problem without requiring a fundamental discretization of spacetime.