Abstract
The problem of the Nature of Time is twofold: whether or not time is a fundamental quantity of Nature, and how does clock time of metrology emerge in the experimental description of dynamics. This work strongly supports the fundamental timelessness of Nature. However, the correct view that physics is described by relations between variables does not addresses the second problem of how time does emerge at the macroscopic scale on the ground of a timeless framework. In this work ordinary Hamiltonian dynamics is first recast in a timeless formalism capable to provide a definition of parameter time on the basis of the only generalized coordinates, together with the Hamiltonian invariance on trajectories, and a variational principle. Next, clock time emerges as a discrete macroscopic quantity by considering subsystems cyclic in the phase space, to which other subsystems refer. Suitable cyclic phenomena, under sufficiently restrictive assumptions on their stability (like atomic clocks) are indeed a good approximation of the canonical parameter time and describe time evolution of physical quantities by means of the same simple dynamical laws.
Enrico Prati