标题： 微观和宏观层次上由于量子效应导致的引力质量与能量的非等价性 显示英文标题

标题： Inequivalence between gravitational mass and energy due to quantum effects at microscopic and macroscopic levels

摘要： 我们回顾了最近的理论结果，证明由于广义相对论中的量子效应，主动引力质量和被动引力质量以及能量之间的等价性被打破。 特别是，我们讨论了最简单的复合量子物体——氢原子，并定义了其引力质量算符。 通过思想实验，我们表明著名的爱因斯坦方程，$E =mc^2$，对于原子的被动引力质量而言，以小概率被破坏。 重要的是，主动和被动引力质量的期望值对于定态量子态满足上述方程。 然而，我们强调，对于氢原子中定态的量子叠加态，其中能量的期望值是常数，质量的期望值随时间振荡，从而破坏爱因斯坦方程。 我们简要讨论了观察上述时间依赖振荡的实验可能性。 在本综述中，我们还改进了原始开创性工作的几个缺点。 显示英文摘要

摘要： 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.