On the Sagnac effect and Quantum Mechanics in a Rotating Reference System

TL;DR

This paper explores quantum mechanics in a rotating system, revealing rotation-induced negative energies and a novel anomalous quantum Sagnac effect through canonical quantization and reanalysis of classical phenomena.

Contribution

It introduces a new approach to compute the quantum Sagnac phase shift and uncovers anomalous effects in rotating quantum systems.

Findings

Existence of rotation-induced negative energy eigenstates.

A novel method to calculate quantum Sagnac phase shift.

Identification of anomalous quantum Sagnac effects in rotating systems.

Abstract

We canonically quantize a spin-less non-relativistic point particle in a rigidly rotating cylinder symmetric reference system. The resulting quantum mechanics is investigated in the case of both a two-dimensional cylindrical shell and in the case of the full rotating cylinder; in both cases energy eigenstates exist which exhibit rotation induced negative energies. Based on a reanalysis of the classical Sagnac effect a novel way to compute the quantum Sagnac phase shift is deduced. It is pointed out that certain states on both the cylindrical shell and in the bulk give rise to a novel anomalous quantum Sagnac effect.