  In conventional path integral quantum mechanics, the integral variables are
the canonical variables of Hamiltonian mechanics. We show that these integral
variables can be transformed into the spacetime metric, leading to a new
representation of quantum mechanics. We show that the wave-particle duality can
be interpreted as the uncertainty of spacetime for the particle. Summarizing
all possible trajectories in conventional path integral quantum mechanics can
be transformed into the summation of all possible spacetime metrics. We
emphasize that in conventional quantum gravity, it is possible that the
classical matter fields correspond to the quantum spacetime. We argue that this
is not quite reasonable and propose a new path integral quantum gravity model
based on the new interpretation of wave-particle duality. In this model, the
aforementioned drawback of conventional quantum gravity naturally disappears.
