The paper by Djordje Minic and Chia-Hsiung Tze presents a detailed derivation of canonical quantum mechanics (QM) based on the compatibility of statistical geometry with Hamiltonian dynamics. This approach naturally extends to a non-perturbative formulation of quantum gravity, which should reduce to general relativity (GR) in the correspondence limit. The authors start by assuming that individual quantum events are statistically distinguishable and introduce the Fisher metric to measure this distinguishability. They then define a canonical Hamiltonian flow on the space of probabilities, leading to the Schrödinger equation. The geometric structure of complex projective spaces (CP(n)) is crucial for understanding the kinematical background of QM. In the context of quantum gravity, the authors extend the postulates of QM to allow for dynamical metrics and symplectic forms on the space of quantum events. This extension is motivated by the need for a quantum version of the equivalence principle. The resulting framework is based on a nonlinear Grassmannian, \( Gr(C^{n+1}) \), which is a symplectic manifold with a non-integrable almost complex structure. This allows for a non-linear "bootstrap" between the space of quantum events and the dynamics, leading to a generalized geodesic Schrödinger equation. The authors suggest that their proposal defines a background-independent, non-perturbative, holographic formulation of Matrix theory. They also discuss possible observational implications, including deviations from the Planck law, the vacuum energy, and the double-slit experiment, as well as the relativity of quantum measurements and deviations from linearity and entanglement.The paper by Djordje Minic and Chia-Hsiung Tze presents a detailed derivation of canonical quantum mechanics (QM) based on the compatibility of statistical geometry with Hamiltonian dynamics. This approach naturally extends to a non-perturbative formulation of quantum gravity, which should reduce to general relativity (GR) in the correspondence limit. The authors start by assuming that individual quantum events are statistically distinguishable and introduce the Fisher metric to measure this distinguishability. They then define a canonical Hamiltonian flow on the space of probabilities, leading to the Schrödinger equation. The geometric structure of complex projective spaces (CP(n)) is crucial for understanding the kinematical background of QM. In the context of quantum gravity, the authors extend the postulates of QM to allow for dynamical metrics and symplectic forms on the space of quantum events. This extension is motivated by the need for a quantum version of the equivalence principle. The resulting framework is based on a nonlinear Grassmannian, \( Gr(C^{n+1}) \), which is a symplectic manifold with a non-integrable almost complex structure. This allows for a non-linear "bootstrap" between the space of quantum events and the dynamics, leading to a generalized geodesic Schrödinger equation. The authors suggest that their proposal defines a background-independent, non-perturbative, holographic formulation of Matrix theory. They also discuss possible observational implications, including deviations from the Planck law, the vacuum energy, and the double-slit experiment, as well as the relativity of quantum measurements and deviations from linearity and entanglement.