Zeno wrote of a lesser known paradox known as The Stadium, meant to disprove the existence of quantized time (though, of course, Zeno didn't use the term quantum). It goes as such:
Consider three ranks of 10 soldiers, lined up as such:
a a a a a a a a a a
b b b b b b b b b b
c c c c c c c c c c
Each soldier is separated by one pace. In the space of a quantum unit of time (the smallest non-divisible unit), rank B takes one pace to the right, while rank C takes one pace to the left. The resulting formation is thus:
a a a a a a a a a a
b b b b b b b b b b
c c c c c c c c c c
The leftmost soldier in rank C is two paces to the left of the leftmost soldier in rank B. At some point in time, in order to get that distance away, C1 had to be one pace to the left of B1. However, the movement took place in the span of a quantum time unit. Therefore, there had to be a smaller possible span of time than the supposed quantum unit.
I've never seen this one disproven; certainly, the math involved would seem to be a bit more involved than with Achilles and the Tortoise. If anyone could find a way to work around this (if one exists), enlighten us. Alternatively, if it can't be explained, then time indeed cannot be quantized.