a world that is infinitely divisible -> a world that is potentially infinitely divisible, I would say.

Quantum means "How much?". Quanta are the fundamental units of something measurable. Measurable implies an instrument that measures. Just because Quantum Physics can't measure it anymore doesn't mean it's not there.

Now, here we leave the realm of science and go into metaphysics. "If we can't measure it, does it still exist?" and the like. "Does it come into existence because we measure it?" If so then we have a potential infinity. Potentially infinite, but is still finite at any given moment. ^_^