Very interesting speculation, Doc. Indeed, if the "resolution were fine enough," discrete "jumps" would look like a continuous process to us. But you suggest there's no "obvious" experiment that could be performed that would allow us to distinguish between the two theories.
But if "there would be no experiment that could give a result that was between one tick and the next," then how could we then demonstrate instances of cause and effect? If the two ticks are separate from each other, how could they affect each other?
Additionally, time divisions could be only countable but dense rather than continuous...the Riemann integral is sufficient for such cases. Continuous time requires a Lesbegue integral. I'm not sure there's an experiment that shows one rather than the other to be "correct."
Thus we have two seemingly mutually exclusive theories and no obvious way to tell which is "correct." (Unless we say that time, like physical particles, has both a discrete and a wave form.)
Maybe these theories aren't testible in themselves, and the only way we can verify or falsify them is to load them into the assumptions of planned experiments and see what happens. But there's a problem even there: How would we know what the experimental results really mean if our assumptions haven't been "validated?" (And then, an even more extreme question: are they even susceptible to validation, in the scientific sense?)
I guess all this shows that "mind" and "matter" interact and can and do modify each other.... And then, perhaps there is the question of what "mind" wants to do here: recover traditional dynamics, or explore the fundamental structure of reality. I suppose motivations get loaded into our assumptions very early on; but this is rarely obvious.
Human beings get a whole lot "right." But sometimes, I wonder how, and why that is....
I wonder if you can help me understand the manner in which a discrete time division would display "density?"
Thank you so much for your fascinating and thought-provoking post, Doc.