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)

1nshepperd8yFor a start the classical hallucination of particles and decay doesn't really
apply at times on the planck scale (since there's no time for the wave to
decohere). There's just the gradual evolution of the quantum wavefunction. It
may be that nothing interesting changes in the wavefunction in less than a
planck time, either because it's actually "blocky" like a cellular automata or
physics simulation, or for some other reason.
In the former case you could imagine that at each time step there's a certain
probability (determined by the amplitude) of decay, such that the expected
(average) time is 0.5 planck times after the expected time of some other event.
Such a setup might well produce the classical illusion of something happening
half a planck time after something else, although in a smeared-out manner that
precludes "exactly".

2[anonymous]8yIn your example you're using the term "now". That term already implies a point
in time and therfore an infinitely divisible time. The problem is that while you
certainly could conceive of a half planck time you could never locate that half
in time. I.e. an event does not happen at a point in time. It happens anywhere
in a given range of time with at least the planck length in extend. Now suppose
that event A happens anywhere in a given timeslice and event B happens in
another timeslice that starts half a planck time after the slice of event A. You
can not say that event B happens half a planck time after event A since the
timeslices overlap and thus you cannot even say that event B happens at all
after event A. It might be the other way round. So while in your mind this half
planck length seems to have some meaning in reality it does not. Your mind
insists on visualizing time as continuous and therefore you can't easily get rid
of the feeling that it were.

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)