  A canonical quantisation of the coordinates of the spacetime within the
general relativity theory is proposed. This quantisation will depend on the
observer but it provides an interesting perspective on the problem of relating
the non-relativistic and classical limits of a possible quantum gravity theory.
In this sense, within this formalism, it is possible to recover from the
quantum equation satisfied by a test field the classical geodesics of the
corresponding spacetime. On the other hand, the Schr\"odinger equation is
recovered in the Newtonian limit. A key ingredient for this procedure is a
generalization of the Maupertuis principle, that is, the possibility of
describing the geodesics of a given metric as the non-affine geodesics of other
conformal metric under the action of a potential.
