Reason of the scaling factor $n^{2}$ in Hydrodynamic limits

Question

In some books about hydrodynamic limits, example De Masi and Pressuti, when taking about the transition from micro to macro to get the hydrodynamic limit of some process it is mentioned that in order to be able to see some movement it is necessary to "rescale" the empirical measure $\pi_{t}^{n}$ by a factor $n^{2} t$. i.e. we end up working with the measure $\pi_{n^{2}t}^{n}$. Why is this rescaling necessary? Sorry if it is a basic question but I really do not get the feeling about it.