Gravitational eigenstates in weak gravity I: dipole decay rates of charged particles

TL;DR

This paper develops analytical formulas for electromagnetic transition rates between gravitational eigenstates of charged particles, revealing that high angular momentum states can have unexpectedly long lifetimes, indicating potential stability in weak gravitational fields.

Contribution

It introduces non-relativistic, analytic expressions for dipole transition rates in gravitational eigenstates, a novel approach in gravitational quantum state analysis.

Findings

High angular momentum states have very long lifetimes.

Some gravitational eigenstates exhibit unexpected stability.

Transition rate formulas enable analysis of gravitational quantum states.

Abstract

The experimental demonstration that neutrons can reside in gravitational quantum stationary states formed in the gravitational field of the Earth indicates a need to examine in more detail the general theoretical properties of gravitational eigenstates. Despite the almost universal study of quantum theory applied to atomic and molecular states very little work has been done to investigate the properties of the hypothetical stationary states that should exist in similar types of gravitational central potential wells, particularly those with large quantum numbers. In this first of a series of papers, we attempt to address this shortfall by developing analytic, non-integral expressions for the electromagnetic dipole state-to-state transition rates of charged particles for any given initial and final gravitational quantum states. The expressions are non-relativistic and hence valid provided the eigenstate wavefunctions do not extend significantly into regions of strong gravity. The formulae may be used to obtain tractable approximations to the transition rates that can be used to give general trends associated with certain types of transitions. Surprisingly, we find that some of the high angular momentum eigenstates have extremely long lifetimes and a resulting stability that belies the multitude of channels available for state decay.