Breakdown of the Einstein's Equivalence Principle for a quantum body

We discuss our recent theoretical results about inequivalence between passive and active gravitational masses and energy in semiclassical variant of General Relativity, where gravitational field is not quantized but matter is quantized. In particular, we consider the simplest composite quantum body - a hydrogen atom. We concentrate our attention on the following physical effects, related to the electron mass. The first one is breakdown of the equivalence between passive gravitational mass and energy at a microscopic level. Indeed, as we show, the quantum measurement of gravitational mass can give result, which is different from the expected, m^g ≠ m_e + E₁/_c² , where electron is initially in its ground state with E = E₁; m_e is the bare electron mass. The second effect is that the expectation values of both passive and active gravitational masses of stationary quantum states are equivalent to the expectation values of energy. The most spectacular effects are inequivalence of passive and active gravitational masses and energy at a macroscopic level for ensembles of the coherent superpositions of stationary quantum states (which we call Gravitational demons). We demonstrate that, for such Gravitational demons, the expectation values of passive and active gravitational masses are not related to the expectation values of energy by the famous Einstein's equation, m^g ≠ E/_c2.