The role of a time parameter is vital to physics, yet time is often taken for granted. Newtonian physics assumes an idealized time variable that is unmeasurable. In this paper, we answer calls for clearer accounts of the emergence of Newtonian time from timeless mechanical systems (Smolin 2013). We consider a three-particle system in the timeless formalism of Jacobi. Time is abstracted from paths in configuration space in accord with Mach’s principle of universal inertial reference frames. This paper makes three contributions to the conversation around time. First, our physical demonstration of how Newtonian time is constructed completes Mach’s arguments about clocks and time in classical, non-relativistic systems. Second, this paper discusses the integration of these ideas regarding time into quantum mechanics. Finally, we answer the question, ‘what do clocks measure?’ using these simple physical systems and use that answer as a foundation for engagement with current metaphysical debates about time.
