AFAIK (pardon my limited knowledge of physical and math terms) the spacetime interval is the conserved unit and it has a lower bound in the Plank-scale limit.
In the paragraph above, you assume time is a primitive concept, but it is really an emergent phenomenon. The passing of time, moving by some amount of (the plank-scale limit of) spacetime interval, can happen only across connected configurations.
Think about evolution in spacetime as a combinatorial game, there can be positions where causal links are not possible, or even empty games.
FWIW I don’t think it’s certain yet that time cannot be divided smaller than the plank limit. I remember reading an article some years ago about an experiment indicating that there seems to be no smallest “slice” of time. Unfortunately I can’t find it and my patience for searching google these days is pretty low.
In the paragraph above, you assume time is a primitive concept, but it is really an emergent phenomenon. The passing of time, moving by some amount of (the plank-scale limit of) spacetime interval, can happen only across connected configurations.
Think about evolution in spacetime as a combinatorial game, there can be positions where causal links are not possible, or even empty games.
The best analogous I can think of arises in the field of surreal numbers https://en.wikipedia.org/wiki/Surreal_number, with their built-in concept of generations.