Reparameterization Invariant Dynamics

Abstract

Abstract For the subset of Jacobi theories where the metric is conformally flat there is always a dynamically privileged ephemeris time parameter that can be defined along a classical curve in terms of the fixed total energy of the system. There are available two importantly different interpretations of the modal status of the total energy constant. Under the first, total energy is interpreted as a constant of nature. The value of the total energy is thus the same for all dynamically possible models with the same token of the constitutive structure. Total energy is therefore a contingently fixed structure of the theory. Under the second, total energy is interpreted as a constant of motion. The value of the total energy is then a free function of the initial data and thus can vary between dynamically possible models with the same token of the constitutive structure.