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, C_{1} had to be one pace to the left of B_{1}. 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.