  A more exotic example involves ‘space invaders’ (Earman 1986: ch. III). These are particles that are at no spatial location at time \(t\), and therefore form no part of the state at time \(t\), but which travel in ‘from’ spatial infinity and by time \(t'\) have a location. We can see the example more clearly if we invoke time-reversal invariance. Consider two point particles, \(a\) and \(b\), at rest and in the vicinity of one another at \(t^*\). From \(t^*\) onwards, force is applied to \(a\) in such a way that the velocity of \(a\) away from \(b\) increases without bound. This is possible, because there is no upper bound on velocity in classical physics. Indeed, let the velocity of \(a\) increase fast enough that by some finite time \(t', a\) has no finite velocity, and is thus ‘at’ spatial infinity. The time-reversal of this system has the particle \(a\) having no location at \(t'\), but having a location and continuously decreasing velocity at every moment \(t \gt t'\), until it comes to rest at \(t^*\). This system violates determinism in the sense given above. The state at \(t'\) consists of a single particle \(b\) at rest. That state could be followed at \(t^*\) by the space-invaded state just described; or it could be followed at \(t^*\) by the incompatible state of \(b\) simply being at rest some more. Nothing in the laws rules out either of these transitions. Of course, the model isn’t particularly physically realistic—where does the force acting on \(a\) come from? But physically more realistic systems exhibiting the same general structure have been given; Earman mentions one due to Mather and McGehee (1975) involving four point particles moving in such a way that the forces they exert on each other in collisions end up unboundedly far from one another in a finite time (see also Saari and Xia 1995).