ABSTRACT
In Newtonian spacetime every point is at a determinate spatial and temporal distance from every other point. In Euclidean plane geometry, transformations that leave the structure of the space unchanged are called 'symmetries'. The distinction between inertial and non-inertial motion is thus preserved: curved paths are followed by accelerating bodies, straight paths by non-accelerating bodies. Robert Geroch says: The Galilean neo-Newtonian view, although it takes a little getting used to, is really a simple and remarkably natural attitude about how space and time operate. The Leibnizian could argue that, provided inter-object spatial relations are retained, the whole system of material bodies could, in each hyper plane, be located at a different and distant collection of spacetime locations. Recent writers have drawn attention to the fundamental incompatibilities between relativity and quantum theory. Maudlin concludes, 'Relations that are sufficiently rich can provide the means for explaining inertial effects'.
