### Abstract

In this paper, 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, (Formula presented.), 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.

Original language | English (US) |
---|---|

Journal | International Journal of Modern Physics D |

DOIs | |

State | Accepted/In press - 2017 |

### Fingerprint

### Keywords

- Equivalence principle
- mass–energy equivalence
- quantum gravity

### ASJC Scopus subject areas

- Mathematical Physics
- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

**Inequivalence between gravitational mass and energy due to quantum effects at microscopic and macroscopic levels.** / Lebed, Andrei G.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Inequivalence between gravitational mass and energy due to quantum effects at microscopic and macroscopic levels

AU - Lebed, Andrei G

PY - 2017

Y1 - 2017

N2 - In this paper, 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, (Formula presented.), 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.

AB - In this paper, 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, (Formula presented.), 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.

KW - Equivalence principle

KW - mass–energy equivalence

KW - quantum gravity

UR - http://www.scopus.com/inward/record.url?scp=85020196026&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85020196026&partnerID=8YFLogxK

U2 - 10.1142/S0218271817300221

DO - 10.1142/S0218271817300221

M3 - Article

AN - SCOPUS:85020196026

JO - International Journal of Modern Physics D

JF - International Journal of Modern Physics D

SN - 0218-2718

ER -