  We review recent theoretical results, demonstrating breakdown of the
equivalence between active and passive gravitational masses and energy due to
quantum effects in General Relativity. In particular, we discuss the simplest
composite quantum body - a hydrogen atom - and define its gravitational masses
operators. Using Gedanken experiment, we show that the famous Einstein's
equation, $E =mc^2$, is broken with small probability for passive gravitational
mass of the atom. It is important that the expectation values of both active
and passive gravitational masses satisfy the above mentioned equation for
stationary quantum states. Nevertheless, we stress that, for quantum
superpositions of stationary states in a hydrogen atom, where the expectation
values of energy are constant, the expectation values of the masses oscillate
in time and, thus, break the Einstein's equation. We briefly discuss
experimental possibility to observe the above-mentioned time-dependent
oscillations. In this review, we also improve several drawbacks of the original
pioneering works.
