This view implies the consistency of the fundamental length/time and Lorentz symmetry, based on the principle of relative (observer-dependent) locality. The geometry of such quantum spacetime is encoded in the new concept of Born geometry. The problem of quantum gravity is then viewed from the perspective of a dynamical Born geometry. In this approach 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 "gravitization of quantum theory''. A specific test of this new approach to quantum gravity is based on intrinsic triple interference in a varying gravitational field, in a profound analogy with recent triple-path interference experiments performed in the context of nonlinear optics.

I will emphasize that the intrinsic 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 in this context as another striking phenomenological probe of gravitization of the geometry of quantum theory.