Breakdown of the equivalence between active gravitational mass and energy for a quantum body

TL;DR

This paper investigates how the active gravitational mass of a quantum system, specifically a hydrogen atom, can deviate from energy equivalence in superposition states, potentially revealing quantum effects in gravity.

Contribution

It introduces a semiclassical approach to analyze the gravitational mass of a quantum body and predicts observable oscillations in gravitational mass for superpositions.

Findings

Expectation value of mass equals energy for stationary states.

Mass expectation oscillates in superpositions, breaking equivalence.

Potential for experimental observation of quantum gravity effects.

Abstract

We determine active gravitational mass operator of the simplest composite quantum body - a hydrogen atom - within the semiclassical approach to the Einstein equation for a gravitational field. We show that the expectation value of the mass is equivalent to energy for stationary quantum states. On the other hand, it occurs that, for quantum superpositions of stationary states with constant expectation values of energy, the expectation values of the gravitational mass exhibit time-dependent oscillations. This breaks the equivalence between active gravitational mass and energy and can be observed as a macroscopic effect for a macroscopic ensemble of coherent quantum states of the atoms. The corresponding experiment could be the first direct observation of quantum effects in General Relativity.