The essay suggests a hypothesis about the nature of space and time. We assume that space is the set of all real numbers, while time is the set of positive real numbers “totally” (“linearly”) ordered in the increasing sense. We support these assumptions by considering some properties of continuous sets and by reinterpreting Dedekind’s axiom of continuity. We also suppose that under specific conditions, which can be found in systems travelling or operating at the speed of light, space and time lose continuity and become one and the same set, that of natural numbers. Lastly, we believe that our perspective may help to clarify some controversial problems of last century's physics, mainly concerning quantum theory.
Giovanni Prisinzano