Breakdown of the equivalence between active gravitational mass and energy for a quantum body

Abstract

We determine active gravitational mass operator of the simplest composite quantum body - a hydrogen atom - within the semiclassical approach to the Einstein equation for a gravitational field. We show that the expectation value of the mass is equivalent to energy for stationary quantum states. On the other hand, it occurs that, for quantum superpositions of stationary states with constant expectation values of energy, the expectation values of the gravitational mass exhibit time-dependent oscillations. This breaks the equivalence between active gravitational mass and energy and can be observed as a macroscopic effect for a macroscopic ensemble of coherent quantum states of the atoms. The corresponding experiment could be the first direct observation of quantum effects in General Relativity.

4 pages

References in corpus (3)

• Breakdown of the equivalence between gravitational mass and energy for a composite quantum body
• Breakdown of the Equivalence between Gravitational Mass and Energy for a Quantum Body: Theory and Suggested Experiments
• Breakdown of the Equivalence between Energy Content and Weight in a Weak Gravitational Field for a Quantum Body

Cited by in corpus (3)

• Inequivalence between gravitational mass and energy due to quantum effects at microscopic and macroscopic levels
• Breakdown of the equivalence between gravitational mass and energy due to quantum effects
• Breakdown of the Einstein's Equivalence Principle for a quantum body