Time and the Deep Structure of Dynamics

Abstract

Newton introduced absolute space in order to have an unambiguous notion of change of position and absolute time to define rates of change. These may be called the Newtonian fundamentals. On the basis of very plausible philosophical principles, Leibniz argued that space is not an entity but merely the instantaneous order of the coexisting things that constitute the universe. Time too is not an entity but merely the succession of states of the universe. In Leibniz’s age, the technical means needed to implement his ideas did not exist, and until recently no systematic attempt was made to create a truly Leibnizian dynamics. I shall show how change of position and the rate at which it occurs can be defined in a Leibnizian ontology provided the universe can be treated as a closed dynam ical system. Mach’s requirement that the local inertial frame of reference arises from the dynamical effect of the universe is automatically satisfied. One can add the further Leibnizian requirement that there should be no instanta- neous action at a distance, that inertial mass must be isotropic, and that future states are defined by the least possible amount of initial data. Then the Leibnizian tools by which the two Newtonian fundamentals are achieved are unique, universal and very characteristic in their structure. In fact, they more or less completely explain the dynamical structure of not only Einstein’s general theory of relativity but also gauge theory. The deep sense in which general relativity is timeless has far-reaching implications for a quantum theory of the universe. If the universe has a wave function, it is highly likely to be static. Thus, Leibnizian ontology leads to a Parmenidean vision of the quantum universe.