The Quantum Closet

TL;DR

This paper derives quantum mechanics from a geometric principle involving Mobius transformations, suggesting space is compact and linking this to energy quantisation and potential cosmological evidence.

Contribution

It introduces a geometric derivation of quantum mechanics based on a cocycle condition invariant under Mobius transformations, implying space compactness and energy quantisation.

Findings

Space is suggested to be compact due to invariance under Mobius transformations.

Energy quantisation naturally arises from the geometric formalism.

Potential cosmological evidence for compactness may be observable in the CMBR.

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.