# Atomic stability and the quantum mass equivalence

## TL;DR

This paper investigates how differences between gravitational and inertial mass could affect atomic stability in gravitational fields, revealing potential long-term instability of hydrogen atoms under certain conditions.

## Contribution

It explores the link between mass equivalence and atomic stability in quantum systems, extending previous studies to internal atomic variables.

## Key findings

- Hydrogen atom becomes unstable in a gravitational field if gravitational mass differs from inertial mass.
- Atomic ionization does not occur in a uniformly accelerated frame regardless of mass equivalence.
- The work extends quantum gravitational studies to internal atomic properties.

## Abstract

We consider an unexplored aspect of the mass equivalence principle in the quantum realm, its connection with atomic stability. We show that if the gravitational mass were different from the inertial one, a Hydrogen atom placed in a constant gravitational field would become unstable in the long term. In contrast, independently of the relation between the two masses, the atom does not become ionized in an uniformly accelerated frame. This work, in the line of previous analyses studying the properties of quantum systems in gravitational fields, contributes to the extension of that programme to internal variables.