And then, we would not call it shaking but bending and twisting, would we?
Think of the 1D variant. If you shuffle a deck of cards, but require that to be ‘continuous’, few shuffles remain (I think only the identity mapping and ‘flipping the deck upside down’). I doubt anybody would restricting the possible permutations that much stil call shuffling.
I think point particles are different because there are infinitely many of them. They are more continuous than cards. This means shaking isn’t necessarily discontinuous even if two particles that were “right next to each other” wind up far apart, there should be more particles in between that ended up closer.
Think of the 1D variant. If you shuffle a deck of cards, but require that to be ‘continuous’, few shuffles remain (I think only the identity mapping and ‘flipping the deck upside down’). I doubt anybody would restricting the possible permutations that much stil call shuffling.