We can think the state of the world is immutable. When the state changes, it's a different world. If space-time is discontinuous, then we can think any change

We can think the state of the world is immutable. When the state changes, it's a different world. If space-time is discontinuous, then we can think any change of state, like motion, as a set of discrete changes. If we think the motion of a particle from one energy bin to another is immediate (meaning the particle cannot be found on the border between the bins, or one moment the particle is in Bin A, next it is in Bin B) then we can think the particle was destroyed in Bin A and another one was created at Bin B. And this is what we call motion from A -> B.