Can a simulation be conducted in which the inhabitants would observe infinite time divisibility? In this video, a physics theorist talks with his collegues claiming to have found evidence for Simulation Theory. I'm not here to ask about the various proofs for and against ST - that's basically in the realm of philosophy at this point.

But one of the physicists claims that because of the nature of mathematics, it's impossible to simulate a particular aspect of our universe: infinite divisibility of time. The theorist responded that math can be used to describe infinite time division, which is all the simulation would need to do. 

My question is this: In Computer Science, can we determine whether it is or is not possible through any currently known medium of computing to create a simulation in which the inhabitants would be able to observe infinite time divisibility?

Elaboration:

If you simulate things at a rate of infinite divisions per second of simulated time, you could never simulate the entire second right? The simulation would hang infinitely? The question is whether you could simulate based on something other than an interval, like in quantum physics, things (seem to) happen more or less precisely on a small level based on whether or not they're being observed (Disclaimer: that's a severe oversimplification).

Whether in CS this method of simulation (resulting in observed but perhaps not literal infinite time divisibility) is fundamentally possible via the computing formats we're aware of is my question. I think it's quite an interesting fundamental CS question. 

Somehow the simulation would have to describe the occurrence of events via functions, not increments, which make it look like to an observer within the simulation that there is no smallest increment.
Yes, you can compute over continuous quantities. Calculus is an example.

If it was actually impossible to compute how a continuous system would behave, then how did this physicist end up believing reality is continuous? How did they make predictions that were confirmed by experiment, scientifically justifying their belief, if they weren't able to calculate any predictions?