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

Abstract

Abstract: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. PACS

Response to: Comment on “Does the Equivalence between Gravitational Mass and Energy Survive for a Composite Quantum Body?”

“…Protons of all atoms are dragged by a spacecraft with constant velocity in the Earth's gravitational field. Due to nonhomogeneous squeezing of space by the gravitational field, the atoms are shown [2,[5][6][7][8] to become excited and emit photons. As mentioned in [5], the above described 2 Advances in High Energy Physics phenomenon is very general and have to be observed in solids, nuclei, and elementary particles.…”

“…Due to nonhomogeneous squeezing of space by the gravitational field, the atoms are shown [2,[5][6][7][8] to become excited and emit photons. As mentioned in [5], the above described 2 Advances in High Energy Physics phenomenon is very general and have to be observed in solids, nuclei, and elementary particles. The main criticism of the experiment [2,[5][6][7][8] in the comment [1] is the statement that the application of our theory to experiments on proton decay is not consistent with the existing experimental data.…”

“…First, we pay attention that the discussed existing experimental data in [1] are obtained for free falling objects. On the other hand, the idealized experiment, suggested by us [2,[5][6][7][8], corresponds to transportation of centers of masses of the hydrogen atoms (i.e., protons) by spacecraft with a constant velocity. We stress that these are two different types of experiments.…”

“…We recall that, so far, quantum effects have been directly tested only in the Newtonian variant of gravitation (see, e.g., [3,4]). In this complex situation, we have recently suggested two novel phenomena [2,[5][6][7][8][9][10]. In particular, we have demonstrated that both passive and active gravitational masses of a composite body are not equivalent to its energy due to some quantum effects.…”

“…In particular, we have demonstrated that both passive and active gravitational masses of a composite body are not equivalent to its energy due to some quantum effects. We have also suggested two experimental ways [2,[5][6][7][8][9][10]] to test the above-mentioned phenomena. If one of such experiments is done, it will be the first direct observation of quantum effects in General Relativity.…”