Non-Relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity

TL;DR

This paper derives the non-relativistic limit of Dirac equations in gravitational fields, explaining gravitational phase effects, bound states, and spin interactions, with implications for astrophysics and quantum gravity experiments.

Contribution

It presents a unified theory-based derivation of the non-relativistic Dirac equation in gravity, revealing quantum gravitational effects and potential observational phenomena.

Findings

Classical Newtonian potential appears in Schrödinger equation with gravity

Quantum particles can form gravitationally bound states detectable in experiments

Gravitomagnetic field couples with quantum spin, producing observable radiation

Abstract

Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we could see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger equation, which can explain the gravitational phase effects found in COW experiments. And because of this Newtonian gravitational potential, a quantum particle in earth's gravitational field may form a gravitationally bound quantized state, which had already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are discussed in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.