TY - JOUR

T1 - Is gravitational mass of a composite quantum body equivalent to its energy?

AU - Lebed, Andrei G.

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

PY - 2013/8

Y1 - 2013/8

N2 - 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.

AB - 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.

KW - equivalence principle

KW - mass-energy equivalence

KW - quantum gravity

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U2 - 10.2478/s11534-013-0302-5

DO - 10.2478/s11534-013-0302-5

M3 - Article

AN - SCOPUS:84886289656

SN - 1895-1082

VL - 11

SP - 969

EP - 976

JO - Central European Journal of Physics

JF - Central European Journal of Physics

IS - 8

ER -