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Quantum Reports

The Violation of the Equivalence Principle for a Composite Quantum Body

A. G. Lebed

Published Aug 26, 2026• 0 citations
Publisher

Abstract

Recently, a publication has appeared that supports the common belief that Einstein’s Equivalence Principle survives for both classical and quantum composite bodies. In contrast, we show that although it holds for classical composite bodies, the Equivalence Principle is broken for composite quantum objects due to the effects of quantum memory. Using the simple example of a hydrogen atom, we demonstrate that the Equivalence Principle is broken for this electron and proton system. We argue that this happens for any composite quantum body.

DOI
10.3390/quantum8030082

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Recently, a publication has appeared that supports the common belief that Einstein’s Equivalence Principle survives for both classical and quantum composite bodies. In contrast, we show that although it holds for classical composite bodies, the Equivalence Principle is broken for composite quantum objects due to the effects of quantum memory. Using the simple example of a hydrogen atom, we demonstrate that the Equivalence Principle is broken for this electron and proton system. We argue that this happens for any composite quantum body.
Recently, we have started to investigate behavior of a composite quantum body in an external gravitational field in the framework of General Relativity [see, for a review, A. G. Lebed, Mod. Phys. Lett. A, {\bf 35}, 2030010 (2020)]. As the simplest example, we have considered a hydrogen atom in a weak gravitational field. Our results are the following. The Einstein's Equivalence Principle survives for the most of macroscopic ensembles of the atoms, containing the stationary quantum states. On the other hand, we have demonstrated that this principle is sometimes broken. In particular, it is broken for the so-called Gravitational demons, which are the coherent macroscopic ensembles of two or more stationary quantum states in the hydrogen atoms. In the above cited paper we have considered the Gedanken experiment, where the gravitational field is suddenly switched on in a free from gravitation space. In the current paper we consider the much more realistic from experimental point of view Gedanken experiment and come to the same conclusion about violations of the Einstein's Equivalence Principle for the Gravitational demons.
We challenge the view that there is a basic conflict between the fundamental principles of Quantum Theory and General Relativity and, in particular, the fact that a superposition of massive bodies would lead to a violation of the Equivalence Principle. It has been argued that this violation implies that such a superposition must inevitably spontaneously collapse (like in the Diósi–Penrose model). We identify the origin of such an assertion in the impossibility of finding a local and classical reference frame in which Einstein's Equivalence Principle would hold. In contrast, we argue that the formulation of the Equivalence Principle can be generalized so that it holds for reference frames that are associated with quantum systems in a superposition of spacetimes. The core of this new formulation is the introduction of a quantum diffeomorphism to such Quantum Reference Frames. This procedure reconciles the principle of linear superposition in Quantum Theory with the principle of general covariance and the Equivalence Principle of General Relativity. Hence, it is not necessary to invoke a gravity-induced spontaneous state reduction when a massive body is prepared in a spatial superposition.
The simplest quantum composite body, a hydrogen atom, is considered in the presence of a weak external gravitational field. We define an operator for the passive gravitational mass of the atom in the post-Newtonian approximation of the general relativity and show that it does not commute with its energy operator. Nevertheless, the equivalence between the expectation values of the mass and energy is shown to survive at a macroscopic level for stationary quantum states. Breakdown of the equivalence between passive gravitational mass and energy at a microscopic level for stationary quantum states can be experimentally detected by studying unusual electromagnetic radiation, emitted by the atoms, supported by and moving in the Earth's gravitational field with constant velocity, using spacecraft or satellite.
Hydrogen atom is studied as a quantum-classical hybrid system, where the proton is treated as a classical object while the electron is regarded as a quantum object. We use a well known mean-field approach to describe this hybrid hydrogen atom; the resulting dynamics for the electron and the proton is compared to their full quantum dynamics. The electron dynamics in the hybrid description is found to be only marginally different from its full quantum counterpart. The situation is very different for the proton: in the hybrid description, the proton behaves like a free particle; in the fully quantum description, the wave packet center of the proton orbits around the center of mass. Furthermore, we find that the failure to describe the proton dynamics properly can be regarded as a manifestation of the fact that there is no conservation of momentum in the mean-field hybrid approach. We expect that such a failure is a common feature for all existing approaches for quantum-classical hybrid systems of Born-Oppenheimer type.
As shown in my previous paper, quantum mechanics (QM) directly violates the weak equivalence principle (WEP) in general, and thus indirectly violates the strong equivalence principle (SEP) in all dimensions. The present paper shows that quantum mechanics also directly violates the SEP unless it is arbitrarily abetted in hindsight. Vital domains are shown to exist in which quantum gravity would be non-applicable. There are classical subtleties in which the SEP appears to be violated, but is not. Neutron free fall interference experiments in a gravitational field are examined, as is Galileo's falling body assertion and the misconception it leads to.
Abstract We propose an experimental test of the quantum equivalence principle introduced by Zych and Brukner (arXiv: 1502.00971 ), which generalises the Einstein equivalence principle to superpositions of internal energy states. We consider a harmonically trapped spin ‐ 1 2 atom in the presence of both gravity and an external magnetic field and show that when the external magnetic field is suddenly switched off, various violations of the equivalence principle would manifest as otherwise forbidden transitions. Performing such an experiment would put bounds on the various phenomenological violating parameters. We further demonstrate that the classical weak equivalence principle can be tested by suddenly putting the apparatus into free fall, effectively ‘switching off’ gravity.