What Is Quantum Theory of Gravity?

We present a line by line derivation of canonical quantum mechanics stemming from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This viewpoint can be naturally extended to provide a conceptually novel, non-perturbative formulation of quantum gravity. Possible observational implications of this new approach are briefly mentioned. 1 What is Quantum Mechanics? In this talk we would like to 1) give a line by line derivation of canonical quantum mechanics (QM) founded on the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics and 2) describe a natural extension of this viewpoint so as to provide a conceptually novel approach to the problem of a non-perturbative formulation of quantum gravity, one which should reduce in the correspondence limit to general relativity (GR) coupled to matter degrees of freedom. The presentation is based on our recent work [1]. To understand the fundamental structure of QM we reason as follows: Assume that individual quantum events are statistical and statistically distinguishable (Postulate I). (This premise is of course a huge conceptual leap in comparison to classical physics, but it is absolutely crucial for the structure of QM.) On the space of probability distributions there is a natural metric, called Fisher metric, which provides a geometric measure of statistical distinguishability [2]