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

Andrei G Lebed

doi:10.1088/1742-6596/738/1/012036

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.

Highlights

The notions of active and passive gravitational masses for a classical composite body are not trivial and have been discussed in recent literature by K
The author of this article has very recently considered quantum case of the simplest composite quantum body - a hydrogen atom [3,4,5,6,7]. He has shown that the quantum virial theorem [8] is responsible for the fact that the expectation values of active and passive gravitational masses of the atom are equivalent to energy for stationary quantum states
As it follows from Eqs.(5),(7), active electron gravitational mass can written in the following way mga =

Summary

INTRODUCTION

The notions of active and passive gravitational masses for a classical composite body are not trivial and have been discussed in recent literature by K. They have stressed that gravitational field is coupled with the following combination: 3K +2U , where K is kinetic and U is potential energies of a composite body. The author of this article has very recently considered quantum case of the simplest composite quantum body - a hydrogen atom [3,4,5,6,7] He has shown that the quantum virial theorem [8] is responsible for the fact that the expectation values of active and passive gravitational masses of the atom are equivalent to energy for stationary quantum states. We discuss possible experiment to discover this breakdown of the Equivalence Principle

ACTIVE GRAVITATIONAL MASS IN CLASSICAL PHYSICS

GRAVITATIONAL MASS IN QUANTUM PHYSICS

SUGGESTED EXPERIMENT