  We tackle the question of motion in Quantum Gravity: what does motion mean at
the Planck scale? Although we are still far from a complete answer we consider
here a toy model in which the problem can be formulated and resolved precisely.
The setting of the toy model is three dimensional Euclidean gravity. Before
studying the model in detail, we argue that Loop Quantum Gravity may provide a
very useful approach when discussing the question of motion in Quantum Gravity.
