Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

On the equivalence principle in quantum theory

Cláus Lämmerzahl

Published May 29, 1996• 90 citations
OpenAlex

Abstract

The role of the equivalence principle in the context of non-relativistic quantum mechanics and matter wave interferometry, especially atom beam interferometry, will be discussed. A generalised form of the weak equivalence principle which is capable of covering quantum phenomena too, will be proposed. It is shown that this generalised equivalence principle is valid for matter wave interferometry and for the dynamics of expectation values. In addition, the use of this equivalence principle makes it possible to determine the structure of the interaction of quantum systems with gravitational and inertial fields. It is also shown that the path of the mean value of the position operator in the case of gravitational interaction does fulfill this generalised equivalence principle.

Related papers

Testing the equivalence principle with atomic interferometry

Sven Herrmann, Hansjörg Dittus, Cláus Lämmerzahl +1 more

The weak equivalence principle (WEP), that is, the universality of free fall, states that all point-like neutral particles in a gravitational field fall in the same way. This is the basis of the geometrization of the gravitational interaction. Together with further requirements on the behavior of point particles, light propagation and clocks one can show that gravity is modeled by a Riemannian geometry. Since in the quantum domain all objects are extended, it is not clear whether the notion of a WEP in the quantum domain makes sense at all. We show that for matter wave interferometry the notion of WEP still can be given a meaning. We give a short overview over schemes which allows a violation of the WEP and emphasize that there are also schemes which show that there might be violations of the WEP in the quantum regime which are not present classically. This makes a test of the WEP with quantum matter necessary. We also give a brief outline of the efforts made for testing the WEP with interferometry with cold atoms in the Bremen drop tower carried out by the QUANTUS and PRIMUS collaboration.

Classical and Quantum Gravity•Aug 15, 2012•57 citations

Quantal Definition of the Weak Equivalence Principle

A. Camacho, Arturo Camacho-Guardian, Kerstin E. Kunze +2 more

The present work analyzes the meaning of the Weak Equivalence Principle in the context of quantum mechanics. A quantal definition for this principle is introduced. This definition does not require the concept of trajectory and relies upon the phase shift induced by a gravitational field in the context of a quantum interference experiment of two coherent beams of particles. In other words, it resorts to wave properties of the system and not to classical concepts as the idea of trajectory.

arXiv:0811.0378•AIP conference proceedings•Jan 1, 2009•3 citations

1 Atom interferometry and the Einstein equivalence principle

Peter Wolf, Luc Blanchet A, Christian J. Borde ́ +3 more

The computation of the phase shift in a symmetric atom interferometer in the presence of a gravitational field is reviewed. The difference of action-phase integrals between the two paths of the interferometer is zero for any Lagrangian which is at most quadratic in position and velocity. We emphasize that in a large class of theories of gravity the atom interferometer permits a test of the weak version of the equivalence principle (or universality of free fall) by comparing the acceleration of atoms with that of ordinary bodies, but is insensitive to that aspect of the equivalence principle known as the gravitational redshift or universality of clock rates.

•Jan 1, 2011•0 citations

Inertial Force, Equivalence Principle and Quantum Mechanics

Minoru Omote, S. Kamefuchi

On the basis of a manifestly covariant formalism of non-relativistic quantum mechanics in general coordinate systems, proposed by us recently, we derive general expressions for inertial forces. The results enable us further to discuss, and to explain the validity of, the equivalence principle in non-relativistic quantum mechanics.

arXiv:quant-ph/0005035•May 10, 2000•0 citations

Entanglement Witness for the Weak Equivalence Principle

Sougato Bose, Anupam Mazumdar, Martine Schut +1 more

The Einstein equivalence principle is based on the equality of gravitational and inertial mass, which has led to the universality of a free-fall concept. The principle has been extremely well tested so far and has been tested with a great precision. However, all these tests and the corresponding arguments are based on a classical setup where the notion of position and velocity of the mass is associated with a classical value as opposed to the quantum entities.Here, we provide a simple quantum protocol based on creating large spatial superposition states in a laboratory to test the quantum regime of the equivalence principle where both matter and gravity are treated at par as a quantum entity. The two gravitational masses of the two spatial superpositions source the gravitational potential for each other. We argue that such a quantum protocol is unique with regard to testing especially the generalisation of the weak equivalence principle by constraining the equality of gravitational and inertial mass via witnessing quantum entanglement.

arXiv:2203.11628•Entropy•Mar 3, 2023•34 citations

Quantum generalisation of Einstein’s equivalence principle can be verified with entangled clocks as quantum reference frames

Carlo Cepollaro, Flaminia Giacomini

Abstract The Einstein equivalence principle (EEP) is of crucial importance to test the foundations of general relativity. When the particles involved in the test exhibit quantum properties, it is unknown whether this principle still holds. A violation of the EEP would have drastic consequences for physics. A more conservative possibility is that the EEP holds in a generalised form for delocalised quantum particles. Here we formulate such a generalised EEP by extending one of its paradigmatic tests with clocks to quantum clocks that are in a quantum superposition of positions and velocities. We show that the validity of such a generalised version of the EEP is equivalent to the possibility of transforming to the perspective of an arbitrary Quantum Reference Frame (QRF), namely a reference frame associated to the quantum state of the clock. We further show that this generalised EEP can be verified by measuring the proper time of entangled clocks in a quantum superposition of positions in the Earth gravitational field. The violation of the generalised EEP corresponds to the impossibility of defining dynamical evolution in the frame of each clock, and results in a modification to the probabilities of measurements calculated in the laboratory frame. Hence, it can be verified experimentally, for instance in an atom interferometer.

arXiv:2112.03303•Classical and Quantum Gravity•Aug 8, 2024•11 citations
The role of the equivalence principle in the context of non-relativistic quantum mechanics and matter wave interferometry, especially atom beam interferometry, will be discussed. A generalised form of the weak equivalence principle which is capable of covering quantum phenomena too, will be proposed. It is shown that this generalised equivalence principle is valid for matter wave interferometry and for the dynamics of expectation values. In addition, the use of this equivalence principle makes it possible to determine the structure of the interaction of quantum systems with gravitational and inertial fields. It is also shown that the path of the mean value of the position operator in the case of gravitational interaction does fulfill this generalised equivalence principle.
The weak equivalence principle (WEP), that is, the universality of free fall, states that all point-like neutral particles in a gravitational field fall in the same way. This is the basis of the geometrization of the gravitational interaction. Together with further requirements on the behavior of point particles, light propagation and clocks one can show that gravity is modeled by a Riemannian geometry. Since in the quantum domain all objects are extended, it is not clear whether the notion of a WEP in the quantum domain makes sense at all. We show that for matter wave interferometry the notion of WEP still can be given a meaning. We give a short overview over schemes which allows a violation of the WEP and emphasize that there are also schemes which show that there might be violations of the WEP in the quantum regime which are not present classically. This makes a test of the WEP with quantum matter necessary. We also give a brief outline of the efforts made for testing the WEP with interferometry with cold atoms in the Bremen drop tower carried out by the QUANTUS and PRIMUS collaboration.
The computation of the phase shift in a symmetric atom interferometer in the presence of a gravitational field is reviewed. The difference of action-phase integrals between the two paths of the interferometer is zero for any Lagrangian which is at most quadratic in position and velocity. We emphasize that in a large class of theories of gravity the atom interferometer permits a test of the weak version of the equivalence principle (or universality of free fall) by comparing the acceleration of atoms with that of ordinary bodies, but is insensitive to that aspect of the equivalence principle known as the gravitational redshift or universality of clock rates.
The Einstein equivalence principle is based on the equality of gravitational and inertial mass, which has led to the universality of a free-fall concept. The principle has been extremely well tested so far and has been tested with a great precision. However, all these tests and the corresponding arguments are based on a classical setup where the notion of position and velocity of the mass is associated with a classical value as opposed to the quantum entities.Here, we provide a simple quantum protocol based on creating large spatial superposition states in a laboratory to test the quantum regime of the equivalence principle where both matter and gravity are treated at par as a quantum entity. The two gravitational masses of the two spatial superpositions source the gravitational potential for each other. We argue that such a quantum protocol is unique with regard to testing especially the generalisation of the weak equivalence principle by constraining the equality of gravitational and inertial mass via witnessing quantum entanglement.
Abstract The Einstein equivalence principle (EEP) is of crucial importance to test the foundations of general relativity. When the particles involved in the test exhibit quantum properties, it is unknown whether this principle still holds. A violation of the EEP would have drastic consequences for physics. A more conservative possibility is that the EEP holds in a generalised form for delocalised quantum particles. Here we formulate such a generalised EEP by extending one of its paradigmatic tests with clocks to quantum clocks that are in a quantum superposition of positions and velocities. We show that the validity of such a generalised version of the EEP is equivalent to the possibility of transforming to the perspective of an arbitrary Quantum Reference Frame (QRF), namely a reference frame associated to the quantum state of the clock. We further show that this generalised EEP can be verified by measuring the proper time of entangled clocks in a quantum superposition of positions in the Earth gravitational field. The violation of the generalised EEP corresponds to the impossibility of defining dynamical evolution in the frame of each clock, and results in a modification to the probabilities of measurements calculated in the laboratory frame. Hence, it can be verified experimentally, for instance in an atom interferometer.