THE MATHEMATICAL STRUCTURE OF NEWTONIAN SPACETIME - CLASSICAL DYNAMICS AND GRAVITATION

We give a precise and modern mathematical characterization of the Newt onian spacetime structure (N). Our formulation clarifies the concepts of absolute space, Newton's relative spaces, and absolute time. The co ncept of reference frames (which are ''timelike'' vector fields on N) plays a fundamental role in ouir approach, and the classification of a ll possible reference frames on N is investigated in detail. We succee d in identifying a Lorentzian structure on N and we study the classica l electrodynamics of Maxwell and Lorentz relative to this structure, o btaining the important result that there exists only one intrinsic gen eralization of the Lorentz force law which is compatible with Maxwell equations. This is at variance with other proposed intrinsic generaliz ation of the Lorentz force law appearing ill the literature. We presen t also a formulation of Newtonian gravitational theory as a curve spac etime theory and discuss its meaning.