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Advances in High Energy Physics
Volume 2014, Article ID 678087, 10 pages
Research Article

Does the Equivalence between Gravitational Mass and Energy Survive for a Composite Quantum Body?

1Department of Physics, University of Arizona, 1118 E. 4th Street, Tucson, AZ 85721, USA
2L. D. Landau Institute for Theoretical Physics, 2 Kosygina Street, Moscow 117334, Russia

Received 7 November 2013; Accepted 21 January 2014; Published 9 March 2014

Academic Editor: Douglas Singleton

Copyright © 2014 A. G. Lebed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


We define passive and active gravitational mass operators of the simplest composite quantum body—a hydrogen atom. Although they do not commute with its energy operator, the equivalence between the expectation values of passive and active gravitational masses and energy is shown to survive for stationary quantum states. In our calculations of passive gravitational mass operator, we take into account not only kinetic and Coulomb potential energies but also the so-called relativistic corrections to electron motion in a hydrogen atom. Inequivalence between passive and active gravitational masses and energy at a macroscopic level is demonstrated to reveal itself as time-dependent oscillations of the expectation values of the gravitational masses for superpositions of stationary quantum states. Breakdown of the equivalence between passive gravitational mass and energy at a microscopic level reveals itself as unusual electromagnetic radiation, emitted by macroscopic ensemble of hydrogen atoms, moved by small spacecraft with constant velocity in the Earth’s gravitational field. We suggest the corresponding experiment on the Earth’s orbit to detect this radiation, which would be the first direct experiment where quantum effects in general relativity are observed.