  It is shown that, with some reasonable assumptions, the theory of general
relativity can be made compatible with quantum mechanics by using the field
equations of general relativity to construct a Robertson-Walker metric for a
quantum particle so that the line element of the particle can be transformed
entirely to that of the Minkowski spacetime, which is assumed by a quantum
observer, and the spacetime dynamics of the particle described by a Minkowski
observer takes the form of quantum mechanics. Spacetime structure of a quantum
particle may have either positive or negative curvature. However, in order to
be describable using the familiar framework of quantum mechanics, the spacetime
structure of a quantum particle must be "quantised" by an introduction of the
imaginary number $i$. If a particle has a positive curvature then the
quantisation is equivalent to turning the pseudo-Riemannian spacetime of the
particle into a Riemannian spacetime. This means that it is assumed the
particle is capable of measuring its temporal distance like its spatial
distances. On the other hand, when a particle has a negative curvature and a
negative energy density then quantising the spacetime structure of the particle
is equivalent to viewing the particle as if it had a positive curvature and a
positive energy density.
