The Quantum Closet

Abstract

The equivalence postulate approach to quantum mechanics entails a derivation of quantum mechanics from a fundamental geometrical principle. Underlying the formalism there exists a basic cocycle condition, which is invariant under D-dimensional finite Mobius transformations. The invariance of the cocycle condition under finite Mobius transformations implies that space is compact. Additionally, it implies energy quantisation and the undefinability of quantum trajectories. I argue that the decompactification limit coincides with the classical limit. Evidence for the compactness of the universe may exist in the Cosmic Microwave Background Radiation.