Orbital angular momentum can take non-integer values in a closed universe

TL;DR

This paper reveals that in a closed universe, orbital angular momentum can have non-integer and irrational values, expanding the traditional quantum mechanical spectrum and potentially affecting cosmological observations.

Contribution

It demonstrates that orbital angular momentum spectra in closed spaces include continuous and irrational values, a novel insight beyond standard integer quantization.

Findings

Orbital angular momentum spectrum includes continuous and irrational values.

The effect is independent of the universe's size.

Potential observable implications in cosmology, such as in the CMB.

Abstract

We show that the spectrum of orbital angular momentum in quantum mechanics consists of two parts when the underlying space has periodic boundaries. While the first part consists of the usual textbook integer quantized values, the second is a continuous band arising from regions at the `edge' of space with respect to the center of rotation. The spectrum thus contains not only half-integer values, previously thought impossible for orbital angular momentum, but even irrational ones. Remarkably, this effect is independent of the size of space. While these spectral components remain undetectable in laboratory experiments, they could still produce observable effects on cosmological scales, for instance in the Cosmic Microwave Background Radiation.