Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Breakdown of the equivalence between gravitational mass and energy due
  to quantum effects   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.

29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph