In this talk I will discuss 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. I will elaborate on a specific test of this new approach to quantum gravity using triple interference in a varying gravitational field. My discussion will be driven by a profound analogy with recent triple-path interference experiments performed in the context of non-linear optics. I will 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. I will also discuss the non-linear Talbot effect as another striking phenomenological probe of gravitization of the geometry of quantum theory.