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

TL;DR

This paper explores the theoretical breakdown of Einstein's Equivalence Principle in certain quantum superpositions of hydrogen atoms, showing that passive gravitational mass may not equal energy divided by c^2 in these cases.

Contribution

It introduces the concept of quantum ensembles, called Gravitational demons, where the equivalence principle is violated, expanding understanding of gravity's interaction with quantum states.

Findings

Most quantum ensembles obey Einstein's Equivalence Principle.

Superpositions of quantum states can break the equivalence principle.

Potential laboratory experiments to test these effects are discussed.

Abstract

We review our recent theoretical results about inequivalence between passive gravitational mass and energy for a composite quantum body at a macroscopic level. In particular, we consider macroscopic ensembles of the simplest composite quantum bodies - hydrogen atoms. Our results are as follows. For the most ensembles, the Einstein's Equivalence Principle is valid. On the other hand, we discuss that for some special quantum ensembles - ensembles of the coherent superpositions of the stationary quantum states in the hydrogen atoms (which we call Gravitational demons) - the Equivalence Principle between passive gravitational mass and energy is broken. We show that, for such superpositions, the expectation values of passive gravitational masses are not related to the expectation values of energies by the famous Einstein's equation, i.e, $m_g \neq \frac{E}{c^2}$. Possible experiments at the Earth's laboratories are briefly discussed, in contrast to the numerous attempts and projects to discover the possible breakdown of the Einstein's Equivalence Principle during the space missions.