Newtownian Relativity, Gravity, and Cosmology

Abstract

Well-known to specialists but little-known to the wider audience is that Newtonian gravity can be understood as geodesic motion in space-time, where time is absolute and space is Euclidean. Newtonian cosmology formulated by Heckmann agrees implicitly with Cartan's formulation of Newtonian mechanics as geodesic motion in space-time, but does not unfold the underlying geometric picture. I present the transformation theory of Newtonian mechanics and gravity developed by Cartan and Heckmann, and show via coordinate transformations that Heckmann's Newtonian cosmological model has a center, so that the cosmological principle cannot hold globally. It is possible to confuse the relativity principle with a position of relativism. Mach's principle has much to do with the latter and nothing to do with the former. Both general relativity and nonlinear dynamics inform us that most coordinate systems ae defined locally by differential equations that are globally nonintegrable: global extensions of local coordinates usually do not exist. I explain how defining inertial frames locally by free fall short-circuits Mach's philosophic objectios to Newtonian dynamics.