The defining property of the Schwarzian derivative in one dimension is its invariance under Mobius transformation. I will describe the relation of the Schwarzian derivative to the formulation of quantum mechanics from an equivalence postulate, which can be viewed as adaptation of the Hamilton Jacobi formalism to quantum mechanics. It yields a cocycle condition which is invariant under D-dimensional Mobious transformations. The invariance under Mobious transformations can only be implemented consistently if space is compact and implies energy quantisation and undefinability of quantum trajectories. It implies the existence of a fundamental length scale that may be identified with the Planck length. Consistency of phase space duality is a complementary facet of the formalism and may serve as the fundamental physical principle underlying quantum mechanics. Evidence for the compactness of space may exist in the cosmic microwave background radiation.