Breakdown of the equivalence between gravitational mass and energy due to quantum effects

TL;DR

This paper reviews recent theoretical findings showing that quantum effects can cause violations of the classical equivalence between gravitational mass and energy, especially in superpositions of quantum states.

Contribution

It demonstrates the breakdown of gravitational mass-energy equivalence at microscopic and macroscopic levels in a semiclassical gravity framework, highlighting new quantum gravitational phenomena.

Findings

Quantum measurement of gravitational mass can differ from classical expectations.

Expectation values of gravitational masses align with energy for stationary states.

Superpositions of quantum states exhibit inequivalence between gravitational mass and energy.

Abstract

We review 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. To this end, we consider the simplest quantum body with internal degrees of freedom - a hydrogen atom. We concentrate our attention on the following physical effects, related to electron mass. The first one is inequivalence between passive gravitational mass and energy at microscopic level. Indeed, quantum measurement of gravitational mass can give result, which is different from the expected, $m \neq m_e + \frac{E_1}{c^2}$, where electron is initially in its ground state; $m_e$ 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 value of energy. The most spectacular effects are inequivalence of passive and active gravitational masses and energy at macroscopic level for ensemble of coherent superpositions of stationary quantum states. We show that, for such superpositions, the expectation values of passive and active gravitational masses are not related to the expectation value of energy by the famous Einstein's equation, $m \neq \frac{E}{c^2}$. In this review, we also improve several drawbacks of the original pioneering works.