Philosophy of Physics: A Very Short Introduction (Very Short Introductions)

by David Wallace

What about the rest-frame structure? It can be thought of as telling us how the points of absolute space themselves evolve in time. Given two points in spacetime—two points on different copies of space—they either represent the same point of absolute space, or different points. This then allows us to define which particle trajectories—which paths through spacetime—represent inertial motion, and which represent accelerated motion. You can think of this as a preferred, special set of paths through spacetime: each one represents a particle at rest. The whole construction—spacetime, the spatial geometry, the temporal metric, and the rest-frame structure—is called Newtonian spacetime, in the normal terminology of philosophy of physics. To do physics, though, we don’t need the rest-frame structure, just the inertial structure, and we can represent this on spacetime by a whole family of preferred, special sets of paths in place of the single set of paths that defined the rest-frame structure. Each member of the family picks out one inertial frame—one collection of particles all moving at the same constant speed—but we don’t regard one as preferred to the others. Doing so makes spacetime a little less structured: the resultant object is called Galilean spacetime, honouring Galileo’s discovery of the relativity principle.

Newtonian (rest frame structure) vs Galilean spacetime (inertial structure)