Motion and the continuum

Motion can easily seem the most unproblematic of phenomena. That things do move seems beyond question: as I watch a car moving along the street, or my hand waving in front of my face, I am literally seeing objects in motion, or so it seems natural to say. Even if, as some would hold (see Chapter 7) it is not strictly speaking correct to say that motion is directly perceived, there is no denying that motion is a ubiquitous feature of everyday life. From a more theoretical standpoint, at least in the context of the simpler and more familiar models of space and time (e.g. flat, Euclidean, Newtonian), motion is equally unproblematic: it is simply a matter of an object varying its location in space over time. In more exotic spacetimes there are additional complications, but much remains unchanged. A spacetime is generally viewed as a structured collection of spacetime points, and whether or not one is moving in a spacetime S will be determined by the trajectory one's worldline takes in S, that is, by the points one's worldline passes through. In spacetimes where motion is relative rather than absolute there is no fact of the matter as to who is really moving, but motion itself is easily discerned: two objects are steadily moving towards one another over an interval t1–t2 if the spatial distance between them is steadily decreasing between t1–t2; they are moving apart from one another if the distance is steadily increasing; and they are at rest relative to one another if the distance is unchanging.