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

arXiv:quant-ph/9612039 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Testing the equivalence principle through freely falling quantum objects

Lorenza Viola, Roberto Onofrio

Published Jan 15, 1997• 129 citations
arXivHTMLPDF

Abstract

Free fall in a uniform gravitational field is reexamined in the case of quantum states with and without a classical analogue. The interplay between kinematics and dynamics in the evolution of a falling quantum test particle is discussed allowing for a better understanding of the equivalence principle at the operational level.
DOI
10.1103/physrevd.55.455

Related papers

Equivalence principle for quantum systems: dephasing and phase shift of free-falling particles

Charis Anastopoulos, B. L. Hu

Abstract We ask the question of how the (weak) equivalence principle established in classical gravitational physics should be reformulated and interpreted for massive quantum objects that may also have internal degrees of freedom (dof). This inquiry is necessary because even elementary concepts like a classical trajectory are not well defined in quantum physics—trajectories originating from quantum histories become viable entities only under stringent decoherence conditions. From this investigation we posit two logically and operationally distinct statements of the equivalence principle for quantum systems. Version A: the probability distribution of position for a free-falling particle is the same as the probability distribution of a free particle, modulo a mass-independent shift of its mean. Version B: any two particles with the same velocity wave-function behave identically in free fall, irrespective of their masses. Both statements apply to all quantum states, including those without a classical correspondence, and also for composite particles with quantum internal dof. We also investigate the consequences of the interaction between internal and external dof induced by free fall. For a class of initial states, we find dephasing occurs for the translational dof, namely, the suppression of the off-diagonal terms of the density matrix, in the position basis. We also find a gravitational phase shift in the reduced density matrix of the internal dof that does not depend on the particle’s mass. For classical states, the phase shift has a natural classical interpretation in terms of gravitational red-shift and special relativistic time-dilation.

arXiv:1707.04526•Classical and Quantum Gravity•Jan 8, 2018•52 citations

Gravitation at the Mesoscopic Scale

Roberto Onofrio, Lorenza Viola

Free fall experiments are discussed by using test masses associated to quantum states not necessarily possessing a classical counterpart. The times of flight of the Galilean experiments using classical test masses are replaced in the quantum case by probability distributions which, although still not defined in an uncontroversial manner, become manifestly dependent upon the mass and the initial state. Such a dependence is also expected in non-inertial frames of reference if the weak equivalence principle still holds. The latter could be tested, merging recent achievements in mesoscopic physics, by using cooled atoms in free fall and accelerated frames initially prepared in nonclassical quantum states.

arXiv:quant-ph/9706004•Modern Physics Letters A•Jun 21, 1997•10 citations

Gravitation at the mesoscopic scale

Roberto Onofrio, Lorenza Viola

Free fall experiments are discussed by using test masses associated to quantum states not necessarily possessing a classical counterpart. The times of flight of the Galilean experiments using classical test masses are replaced in the quantum case by probability distributions which, although still not defined in an uncontroversial manner, become manifestly dependent upon the mass and the initial state. Such a dependence is also expected in non-inertial frames of reference if the weak equivalence principle still holds. The latter could be tested, merging recent achievements in mesoscopic physics, by using cooled atoms in free fall and accelerated frames initially prepared in nonclassical quantum states.

•Jan 1, 1997•5 citations

On free fall of quantum matter

Viacheslav A. Emelyanov

Abstract We propose an approach that allows to systematically take into account gravity in quantum particle physics. It is based on quantum field theory and the general principle of relativity. These are used to build a model for quantum particles in curved spacetime. We compute by its means a deviation from a classical geodesic in the Earth’s gravitational field. This shows that free fall depends on quantum- matter properties. Specifically, we find that the free-fall universality and the wave-packet spreading are mutually exclusive phenomena. We then estimate the Eötvös parameter for a pair of atoms freely falling near the Earth’s surface, provided that the wave-packet spreading is more fundamental than the weak equivalence principle.

arXiv:2110.10056•The European Physical Journal C•Apr 11, 2022•12 citations

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

Quantum coupling between gravity and mass in bouncing ball dynamics

A. Feoli, Elmo Benedetto, Fabiano Feleppa

Abstract We review the dynamics of a bouncing ball, both from the classical and the quantum points of view, studying the role of its inertial and gravitational masses. We analyze the behavior of quantum particles of different masses, embedded in a uniform gravitational field. We show that the bouncing ball is a useful didactic example to show that the coupling between rest mass and gravity cannot be avoided at the quantum level and that the equivalence principle must be reformulated in quantum mechanics. Galileo’s experiment of falling bodies can be still satisfied if one considers only the average quantum values of observables.

European Journal of Physics•Nov 15, 2018•5 citations
Abstract We ask the question of how the (weak) equivalence principle established in classical gravitational physics should be reformulated and interpreted for massive quantum objects that may also have internal degrees of freedom (dof). This inquiry is necessary because even elementary concepts like a classical trajectory are not well defined in quantum physics—trajectories originating from quantum histories become viable entities only under stringent decoherence conditions. From this investigation we posit two logically and operationally distinct statements of the equivalence principle for quantum systems. Version A: the probability distribution of position for a free-falling particle is the same as the probability distribution of a free particle, modulo a mass-independent shift of its mean. Version B: any two particles with the same velocity wave-function behave identically in free fall, irrespective of their masses. Both statements apply to all quantum states, including those without a classical correspondence, and also for composite particles with quantum internal dof. We also investigate the consequences of the interaction between internal and external dof induced by free fall. For a class of initial states, we find dephasing occurs for the translational dof, namely, the suppression of the off-diagonal terms of the density matrix, in the position basis. We also find a gravitational phase shift in the reduced density matrix of the internal dof that does not depend on the particle’s mass. For classical states, the phase shift has a natural classical interpretation in terms of gravitational red-shift and special relativistic time-dilation.
Free fall experiments are discussed by using test masses associated to quantum states not necessarily possessing a classical counterpart. The times of flight of the Galilean experiments using classical test masses are replaced in the quantum case by probability distributions which, although still not defined in an uncontroversial manner, become manifestly dependent upon the mass and the initial state. Such a dependence is also expected in non-inertial frames of reference if the weak equivalence principle still holds. The latter could be tested, merging recent achievements in mesoscopic physics, by using cooled atoms in free fall and accelerated frames initially prepared in nonclassical quantum states.
Free fall experiments are discussed by using test masses associated to quantum states not necessarily possessing a classical counterpart. The times of flight of the Galilean experiments using classical test masses are replaced in the quantum case by probability distributions which, although still not defined in an uncontroversial manner, become manifestly dependent upon the mass and the initial state. Such a dependence is also expected in non-inertial frames of reference if the weak equivalence principle still holds. The latter could be tested, merging recent achievements in mesoscopic physics, by using cooled atoms in free fall and accelerated frames initially prepared in nonclassical quantum states.
Abstract We propose an approach that allows to systematically take into account gravity in quantum particle physics. It is based on quantum field theory and the general principle of relativity. These are used to build a model for quantum particles in curved spacetime. We compute by its means a deviation from a classical geodesic in the Earth’s gravitational field. This shows that free fall depends on quantum- matter properties. Specifically, we find that the free-fall universality and the wave-packet spreading are mutually exclusive phenomena. We then estimate the Eötvös parameter for a pair of atoms freely falling near the Earth’s surface, provided that the wave-packet spreading is more fundamental than the weak 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.
Abstract We review the dynamics of a bouncing ball, both from the classical and the quantum points of view, studying the role of its inertial and gravitational masses. We analyze the behavior of quantum particles of different masses, embedded in a uniform gravitational field. We show that the bouncing ball is a useful didactic example to show that the coupling between rest mass and gravity cannot be avoided at the quantum level and that the equivalence principle must be reformulated in quantum mechanics. Galileo’s experiment of falling bodies can be still satisfied if one considers only the average quantum values of observables.