The Fundamental Problem of Dynamics

Abstract

In a world in which all objects are in relative motion, there arises the problem of equilocality: the identification of points in space that have the same position at different times. Newton recognized this as the fundamental problem of dynamics and to solve it introduced absolute space. Inspired by Mach, Einstein created general relativity in the hope of eliminating this controversial concept, but his indirect approach left the issue unresolved. I will explain how the general method of best matching always leads to dynamical theories with an unambiguous notion of equilocality. Applied to the dynamics of Riemannian 3-geometry, it leads to a radical rederivation of general relativity in which relativity of local scale replaces replaces relativity of simultaneity as a foundational principle. Whereas in the standard spacetime picture there is no unique notion of simultaneity or history, if this alternative derivation leads to the physically correct picture both are fixed in the minutest detail. New approaches to several outstanding problems, including singularities and the origin of time’s arrows, are suggested.