  Recently we have discussed a new approach to the problem of quantum gravity
in which the quantum mechanical structures that are traditionally fixed, such
as the Fubini-Study metric in the Hilbert space of states, become dynamical and
so implement the idea of gravitizing the quantum. In this paper we elaborate on
a specific test of this new approach to quantum gravity using triple
interference in a varying gravitational field. Our discussion is driven by a
profound analogy with recent triple-path interference experiments performed in
the context of non-linear optics. We emphasize that the triple interference
experiment in a varying gravitational field would deeply influence the present
understanding of the kinematics of quantum gravity and quantum gravity
phenomenology. We also discuss the non-linear Talbot effect as another striking
phenomenological probe of gravitization of the geometry of quantum theory.
