The mathematical structure of newtonian spacetime - classical dynamics and gravitation

We give a precise and modern mathematical characterization of the Newtonian spacetime structure (N). Our formulation clarifies the concepts of absolute space, Newton's relative spaces, and absolute time. The concept of reference frames (which are ''timelike'' vector fields on N) plays a fundamental role in ouir approach, and the classification of all possible reference frames on N is investigated in detail. We succeed in identifying a Lorentzian structure on N and we study the classical electrodynamics of Maxwell and Lorentz relative to this structure, obtaining the important result that there exists only one intrinsic generalization of the Lorentz force law which is compatible with Maxwell equations. This is at variance with other proposed intrinsic generalization of the Lorentz force law appearing ill the literature. We present also a formulation of Newtonian gravitational theory as a curve spacetime theory and discuss its meaning.We give a precise and modern mathematical characterization of the Newtonian spacetime structure (N). Our formulation clarifies the concepts of absolute space, Newton's relative spaces, and absolute time. The concept of reference frames (which are ''timeli256871924FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOSEM INFORMAÇÃOSEM INFORMAÇÃ