Another cause/fix to it is to do with quantisation, and quantum physics.
This lead to a similar paradox called the UV catastrophe.

The premise was you could infinitely divide things, time and distance, so half of whatever measurement there is, but it turns out you can only get so far, and then it blends together in the Planck length and Planck-time.
It's not a case of just being the smallest thing currently measurable, it's more the limit on the granularity of the universe.

The UV catastrophe is what started quantum physics, the maths said that a black body (in simple words, something that radiates heat perfectly) would radiate energy at all different frequencies in differing levels. The maths divided these frequencies infinitely, and they all had at least some energy, at that would mean it would radiate infinite energy too.
It was figured out that you couldn't just divide everything infinitely, it got down to discrete quantised steps, eg mini packets or "quanta" in these levels.

The Planck length is the smallest possible division of space and distance, and you can't halve it, and the Planck time is the time it takes light to cover the Planck distance, eg the fastest possible thing covering the smallest possible distance, and it can't get smaller.