Classical mechanics with rational coordinates instead of real

[Shing]

Classical Mechanics define our space is $E^3$
that's also assumed to be $R^3$x $R_t$
I just wondering what if $Q^3$x $Q_t$?
will it make any significant difference? will it cause any logical paradox?

thanks for reading!

 

[CompuChip]

The first thing I wonder about is how a particle in one dimension will get from coordinate a to coordinate b. In my mind, it should always do so in a continuous fashion. But you suppose it would "hop" from one rational to the "next"? You would solve Newton's laws (like F = m x'') in an interval with "holes" (e.g. $[a, b] \cap \mathbb{Q}$)?