TY - JOUR

T1 - Breakdown of the equivalence between gravitational mass and energy for a quantum body

T2 - Theory and suggested experiments

AU - Lebed, Andrei G.

N1 - Funding Information:
We are thankful to N. N. Bagmet (Lebed), V. A. Belinski, Steven Carlip, Fulvio Melia, Douglas Singleton and V. E. Zakharov for fruitful and useful discussions. This work was supported by the NSF under Grant DMR-1104512.

PY - 2015/10/1

Y1 - 2015/10/1

N2 - In this paper, we review recent theoretical results, obtained for the equivalence between gravitational mass and energy of a composite quantum body as well as for its breakdown at macroscopic and microscopic levels. In particular, we discuss that the expectation values of passive and active gravitational mass operators are equivalent to the expectation value of energy for electron stationary quantum states in hydrogen atom. On the other hand, for superpositions of the stationary quantum states, inequivalence between the gravitational masses and energy appears at a macroscopic level. It reveals itself as time-dependent oscillations of the expectation values of passive and active gravitational masses, which can be, in principle, experimentally measured. Inequivalence between passive gravitational mass and energy at a microscopic level can be experimentally observed as unusual electromagnetic radiation, emitted by a macroscopic ensemble of the atoms. We propose the corresponding experiment, which can be done on the Earth's orbit, using small spacecraft. If such experiment is done it would be the first direct observation of quantum effects in general relativity.

AB - In this paper, we review recent theoretical results, obtained for the equivalence between gravitational mass and energy of a composite quantum body as well as for its breakdown at macroscopic and microscopic levels. In particular, we discuss that the expectation values of passive and active gravitational mass operators are equivalent to the expectation value of energy for electron stationary quantum states in hydrogen atom. On the other hand, for superpositions of the stationary quantum states, inequivalence between the gravitational masses and energy appears at a macroscopic level. It reveals itself as time-dependent oscillations of the expectation values of passive and active gravitational masses, which can be, in principle, experimentally measured. Inequivalence between passive gravitational mass and energy at a microscopic level can be experimentally observed as unusual electromagnetic radiation, emitted by a macroscopic ensemble of the atoms. We propose the corresponding experiment, which can be done on the Earth's orbit, using small spacecraft. If such experiment is done it would be the first direct observation of quantum effects in general relativity.

KW - Mass-energy equivalence

KW - equivalence principle

KW - quantum gravity

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U2 - 10.1142/S021827181530027X

DO - 10.1142/S021827181530027X

M3 - Review article

AN - SCOPUS:84938854353

VL - 24

JO - International Journal of Modern Physics D

JF - International Journal of Modern Physics D

SN - 0218-2718

IS - 11

M1 - 1530027

ER -