Abstract

Some experimental theories of quantum gravity, such as loop quantum gravity, propose a discrete or ``quantized'' structure for space-time at very small scales. These theories hypothesize that space-time is fundamentally made up of discrete units or ``atoms'' of space, in a similar way to how matter is fundamentally made up of discrete particles. In the context of space-time, the term ``atomic structure'' is used metaphorically to suggest a discrete or granular nature at extremely small scales. In Einstein's special theory of relativity, there is a maximum limit of speed, beyond which no point of mass in an inertial reference frame can travel. In the following, I will demonstrate that in a given inertial reference frame, in addition to the existence of an upper limit velocity of the motion of a point of mass, there are also logical reasons to think that space and time have an atomic structure. The basic idea of this argument was suggested by Zeno's well-known aporias.