Consider a small, spatially finite possible world that is divided into three zones, A, B, and C. In Zone A, there is a complete freeze — a cessation of all change — for one hour every 2 years. These local freezes in Zone A are preceded by a short period in which every object in A takes on a reddish glow (observable to the occupants of all three zones), while at the same time a temporary force field develops at the boundary of Zone A, preventing anything from entering or exiting that zone during the freeze. While the freeze in Zone A is taking place, Zone A appears to those in Zones B and C to be pitch black, since no light can enter or exit the frozen zone; but as soon as the local freeze in Zone A is over, the people in the other two zones can again see everything in Zone A, and can in fact see those things resuming their normal behaviors without missing a beat. To those who remain in Zone A for the freeze, it appears that the reddish glowing and the development of the force field are immediately followed, not by any cessation of change, but, instead, by a large number of sudden and discontinuous changes in the other two zones.
Meanwhile, In Zone B there is a similar freeze for one hour every 3 years, and in Zone C there is a freeze for one hour every 5 years. The inhabitants of this strange world quickly become aware of the local freezes, and they have no trouble calculating the “freeze function” for each of the three zones. What’s more, they also calculate that there is a global freeze — a period during which each one of the three zones undergoes a local freeze — exactly once every 30 years. Whenever a global freeze occurs, of course, no one is able to see any frozen objects or blacked-out zones, since everyone and everything is frozen at the same time. But the reddish glowing and the development of temporary force fields that precede each world-wide freeze are observable to everyone; and so the global freeze times come to be celebrated by “empty time parties” all over the world.
No doubt the inhabitants of this unusual world could come up with a theory that explains the local freezes in a way that doesn’t posit any empty time. For they could theorize that in Zone A there is a local freeze every two years, except for the 30th year, when there is no freeze; and similarly for the other zones. But such a theory would involve freezing functions that are more complicated than those that entail a global freeze every 30 years.
What is this thought experiment supposed to show? Well, it can’t be taken to show that global freezes are possible, because (at least the way the story has been told here) they are simply a stipulated detail of the story, and we can’t show that something is possible merely by stipulating that it is the case in some possible world. What the thought experiment does seem to show, however, is that it is possible for rational beings to have at least some evidence for the existence of periods of empty time in their world. For we can describe the possible world of the thought experiment in a neutral way that specifies how things in the world appear to its denizens, without specifying whether the real freeze functions for Zones A, B, and C are the simpler ones described above that entail a global freeze every 30 years or the more complicated ones that do not have that entailment. And a possible world that appears this way to its inhabitants is surely a world in which those inhabitants have some reason to take seriously the possibility that there are periods of empty time in their world, that they know when those periods occur, and even that they know exactly how long the periods of empty time last.