Unless space-time is quantized.

My mind just exploded. Would you have to breach a threshold to jump to the next state?

From my understanding, you start with a 0% chance to be in one state and 100%[1] to be in the other. Then the probability starts shifting more and more, till it is the other way around.

At least that is what I think it is, due to me having a very limited amount of knowledge in quantum physics. If a expert could confirm/deny my reasoning, it'd be appreciated.

[1] That is probably an exagerration as it would likely span more than just 2 possible states at any one time, but I chose two as a way to make it more understandable.

It’s true for converting liquid into gas.

So we could measure its movement in arc-Plancks?

Assuming the query [10^100 planck lengths to lightyears] is a correct interpretation of the question, a tooth on the first gear would need to move ~10^49 light years (well, in a circle) before a tooth on the last gear moved 1 Planck length.

I am less familiar with arc-Plancks, but I assume that is sufficient to say "the last gear doesn't move".