 spatio-temporal geometry best suited to describe the universe is fixed together with the dynamical laws by the history of these relations as a whole. Given the fact that the change in the distance relations manifests certain salient patterns, Huggett singles out the notion of inertial motion as the idea of a particularly regular and simple motion. He then ties the notion of reference frame to that of a material body at rest at the origin of the frame. This makes it possible to relate different frames by means of continuous spatially rigid transformations. An inertial frame can then be defined as the frame in which the dynamical laws that supervene on the history of relations for the entire universe hold. In this way, the notion of inertial motion neither requires a substantival affine structure that singles out straight trajectories nor an absolute external time to which the uniformity of motion should be referred. Rather, these two structures supervene on purely relational facts. By the same token, absolute acceleration is reduced to the history of change of the spatial relations holding between an inertial and a non-inertial frame. Similarly, the regularities in the history of relations make it that Euclidean geometry is the simplest and most informative geometry representing that history. Such a framework clearly vindicates Leibnizian relationalism about space (spatial relations and their change are the ontological bedrock) and time (temporal facts supervene on the history, i.e. an ordered sequence, of instantaneous distance relations).

In the same vein, @Hall:2009aa [§ 5.2] sketches out how dynamical parameters such as both inertial and gravitational mass as well as charge can be introduced as variables that figure in the laws of classical mechanics achieving the simplest and most informative description of the change in the relative particle positions throughout the history of the universe. Furthermore, this strategy has recently been applied to the quantum theories that admit a primitive ontology of matt