Breakdown of the Equivalence between Gravitational Mass and Energy for a Quantum Body: Theory and Suggested Experiments

TL;DR

This paper reviews theoretical findings on the breakdown of the equivalence between gravitational mass and energy in quantum systems, proposing experiments to observe quantum gravitational effects.

Contribution

It introduces a theoretical framework showing when and how gravitational mass and energy equivalence breaks down in quantum states, and suggests feasible experiments to detect these effects.

Findings

Expectation values of gravitational masses match energy in stationary states.

Superpositions cause time-dependent oscillations in gravitational mass expectation values.

Proposed experiments could observe quantum gravitational effects on Earth's orbit.

Abstract

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 masses operators are equivalent to the expectation value of energy for electron stationary quantum states in a 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.