2. Reformulating Physics Without Time

Time is an effective concept generated by the development of human natural languages and reinforced by its practical success when used to simplify the description of macroscopic bodies. After the advent of the scientific method, time has occupied a formal role started by the laws of classical dynamics. It has led to the concept of causality by combining it with the principle of induction. At a fundamental level, the extension of such concept out of the natural language to foundations of physics generates tautologies, paradoxes, contradictions, and it limits the ultimate comprehension of nature. I show that even the operative definition of time based on a pair of atomic clocks is a tautology which could be circumvented by using only space-related concepts. On the other hand, using time is not a necessary requirement to describe dynamics, for instance, by the Hamiltonian formalism. Indeed, by applying a variational principle, a natural timeless parametrization of the trajectory in the phase space arises. I show how to fill the gap by the timelessness of fundamental physics by replacing the concept of periodicity in time with cyclicity in the phase space. The connection is completed by defining subsystems acting as generalized clocks with respect to which the description of dynamics of the other subsystems becomes simple.