GALILEAN METRIC GRAVITY

The pressure of empirical circumstance has led to the consensus that theories of gravitation must almost certainly be metric theories if they are to be successful, and the modern perception is that such metric theories can only have meaning within the general context of space-time physics with its associated concepts of curved space-time manifolds. However, this latter perception, where it exists, is rooted in the historical development of the subject and is not informed by any empirical circumstance. Correspondingly, the immediate purpose of the presented paper is to show that metric gravity, as a general concept, is implicitly contained in the idea of the momentum-conserving interaction and is independent of all additional concepts; this, of course, implies that concepts of curved space-time manifolds are strictly superfluous to the function of describing gravitational physics. The basic idea is realizable within the context of either Newtonian mechanics in Galilean space and time or Einstein's relativistic mechanics in Lorentzian space-time, and is illustrated here for the physics of Galileo and Newton; in particular it is shown how Newton's universal theory of gravitation arises as a special case of this analysis.