On the gravitomagnetic clock effect in quantum mechanics

TL;DR

This paper explores how the classical gravitomagnetic clock effect can be extended into quantum mechanics, proposing a semi-classical calculation that links energy level splitting to the clock effect.

Contribution

It introduces a semi-classical approach to calculate the gravitomagnetic clock effect in quantum mechanics and draws an analogy between energy level splitting and the classical clock effect.

Findings

The calculation is valid in the semi-classical regime.

Energy level splitting corresponds to the classical clock effect.

Lays groundwork for a quantum theory of gravitomagnetism.

Abstract

In this article, we discuss how to carryover gravitomagnetic clock effect from classical general relativity to quantum theory and how to calculate this effect in quantum mechanics. Our calculation is valid for semi-classical regime and can be considered as the first step towards a complete gravitomagnetic quantum theory. We also show the analogy between energy levels that corresponds to the clock effect. In fact, it is argued that in quantum mechanics clock effect arises as energy level splitting in gravitomagnetic field.