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Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

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Volume 11, Issue 8


Volume 13 (2015)

Is gravitational mass of a composite quantum body equivalent to its energy?

Andrei Lebed
  • Department of Physics, University of Arizona, 1118 E. 4-th Street, Tucson, AZ, 85721, USA
  • L.D. Landau Institute for Theoretical Physics, RAS, 2 Kosygina Street, 117334, Moscow, Russia
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Published Online: 2013-10-23 | DOI: https://doi.org/10.2478/s11534-013-0302-5


We define passive gravitational mass operator of a hydrogen atom in the post-Newtonian approximation of general relativity and show that it does not commute with energy operator, taken in the absence of gravitational field. Nevertheless, the equivalence between the expectation values of passive gravitational mass and energy is shown to survive for stationary quantum states. Inequivalence between passive gravitational mass and energy at a macroscopic level results in time dependent oscillations of the expectation values of passive gravitational mass for superpositions of stationary quantum states, where the equivalence restores after averaging over time. Inequivalence between gravitational mass and energy at a microscopic level reveals itself as unusual electromagnetic radiation, emitted by the atoms, supported and moved in the Earth gravitational field with constant velocity using spacecraft or satellite, which can be experimentally measured.

Keywords: equivalence principle; quantum gravity; mass-energy equivalence

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About the article

Published Online: 2013-10-23

Published in Print: 2013-08-01

Citation Information: Open Physics, Volume 11, Issue 8, Pages 969–976, ISSN (Online) 2391-5471, DOI: https://doi.org/10.2478/s11534-013-0302-5.

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© 2013 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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