I've read that too, but I get confused when I try to use this fact to answer the question. On the one hand, it seems you are right that nothing can happen in a time shorter than the Planck time, but on the other hand, we seem to rely on the infinite divisibility of time just in making this claim. After all, it's perfectly intelligible to talk about a span of time that is one half or one quarter of Planck time. There's no contradiction in this. The trouble is that nothing can happen in this time, or as you put it, that it cannot be meaningful. But does this last point mean that there is no shorter time, given that a shorter time is perfectly intelligible?
Suppose for example that exactly 10 planck times from now, a radium atom begins decay. Exactly 10 and a half planck times from now, another radium atom decays. Is there anything problematic in saying this? I've not said that anything happened in less than a Planck time. 10 Planck times and 10.5 Planck times are both just some fraction of a second and both long enough spans of time to involve some physical change. If there's nothing wrong with saying this, then we can say that the first atom began its decay one half planck length before the second. This makes a half Planck length a meaningful span of time in describing the relation between two physical processes.
Well, the correct answer up to this point is that we don't know. We would need a theory of quantum gravity to understand what's happening at this scale, and who knows how many ither step further we need to move to have a grasp of the "real" answer. Up to now, we only know that "something" is going to happen, and can make (motivated) conjectures.
It may indeed be that time is discretized in the end, and talking about fractions of planck time is meaningless: maybe the universe computes the next state based on the present one in discrete s... (read more)