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:1502.07875 · Classical and Quantum Gravity

Effect of quantum statistics on the gravitational weak equivalence principle

S V Mousavi, A S Majumdar, D Home

Published Oct 9, 2015• 7 citations
arXivHTMLPDF

Abstract

Abstract We study the effect of quantum statistics on the arrival time distribution of quantum particles computed through the probability current density. It is shown that symmetrization or asymmetrization of the wave function affects the arrival time distribution for even freely propagating particles. In order to investigate the effect of statistics on the weak equivalence principle in quantum mechanics (WEQ), we then compute the mean arrival time for wavepackets in free fall. The violation of WEQ through the effect of statistics on the mass dependence of the mean arrival time is clearly exhibited. We finally evaluate the effect of spin on the violation of WEQ using a different approach by including an explicit spin-dependence in the probability current distribution, and compare it with the approach using particle statistics. Our results show WEQ re-emerges smoothly in the limit of large mass.

DOI
10.1088/0264-9381/32/21/215014

Related papers

Equivalence principle and quantum statistics

A.S. Majumdar, S.V. Mousavi, D. Home

Violation of the gravitational weak equivalence principle in quantum mechanics (WEQ) has been earlier studied using Gaussian wave packets in free fall.Here we study the effect of quantum statistics on the -Gaussian as well as non rrival time distribution of quantum particles computed through the probability current density.We show that a symmetrization or asymmetrization of the wave function impacts the arrival time distribution of wavepackets.The . the mass of the particles, and varies according to the statistics mean arrival time is dependent on

Physical Interpretation of Relativity Theory Proceedings of International Meeting•Dec 1, 2015•0 citations

Strong quantum violation of the gravitational weak equivalence principle by a non-Gaussian wave packet

P Chowdhury, D Home, A S Majumdar +3 more

The weak equivalence principle of gravity is examined at the quantum level in two ways.First, the position detection probabilities of particles described by a non-Gaussian wave packet projected upwards against gravity around the classical turning point and also around the point of initial projection are calculated.These probabilities exhibit mass dependence at both these points, thereby reflecting the quantum violation of the weak equivalence principle.Second, the mean arrival time of freely falling particles is calculated using the quantum probability current, which also turns out to be mass dependent.Such a mass dependence is shown to be enhanced by increasing the non-Gaussianity parameter of the wave packet, thus signifying a stronger violation of the weak equivalence principle through a greater departure from Gaussianity of the initial wave packet.The mass dependence of both the position detection probabilities and the mean arrival time vanishes in the limit of large mass.Thus, compatibility between the weak equivalence principle and quantum mechanics is recovered in the macroscopic limit of the latter.A selection of Bohm trajectories is exhibited to illustrate these features in the free fall case.

arXiv:1107.5159•Classical and Quantum Gravity•Dec 23, 2011•15 citations

Quantum free-fall motion and quantum violation of the weak equivalence principle

Philip Caesar Flores, Eric A. Galapon

The weak equivalence principle (WEP) in the quantum regime has been the subject of many studies with a broad range of approaches to the problem. Here, we tackle the problem anew through the time of arrival (TOA) operator approach. This is done by constructing the TOA operator for a nonrelativistic and structureless particle that is projected upward in a uniform gravitational field with an intended arrival point below the classical turning point. The TOA operator is constructed under the constraint that the inertial and gravitational masses are equivalent and that Galilean invariance is preserved. These constraints are implemented by Weyl quantization of the corresponding classical TOA function for the projectile. The expectation value of the TOA operator is explicitly shown to be equal to the classical time of arrival plus mass-dependent quantum correction terms, implying incompatibility of the WEP with quantum mechanics. The full extent of the violation of the WEP is shown through the mass dependence of TOA distribution for the projectile.

arXiv:1808.02646•Physical Review A•Apr 17, 2019•16 citations

Adherence and violation of the equivalence principle from classical to quantum mechanics

Joseph Balsells, Martin Bojowald A

Investigation into the applicability of the equivalence principle in quantum mechanics has taken many forms, with varying conclusions. Here, a dynamical semiclassical description of a wave packet in terms of its center of mass and higher quantum fluctuations is applied to the case of a quantum particle in gravitational free fall. The analysis provides an intuitive account of the origin of mass dependence in quantum-gravitational dynamics through an effective potential that enforces the uncertainty principle. This potential has two implications: (i) The lowest order quantum fluctuations encoding the width and spreading of the wave packet obey an uncertainty relation whose observance is mass dependent. (ii) In an inhomogeneous gravitational field tidal effects couple the center of mass motion to the quantum fluctuations. The combined effect results in a clear demonstration of how some conceptions of the weak equivalence principle, based on mass dependence, are violated. The size of this violation is within sensitivities of current E\"otv\"os and clock-based return time experiments.

arXiv:2310.09218•Physical review. D/Physical review. D.•Oct 13, 2023•2 citations

Quantum Mechanics and the Weak Equivalence Principle

Stella Huérfano, Sarira Sahu, M. Socolovsky

We use the Feynman path integral approach to nonrelativistic quantum mechanics twofold. First, we derive the lagrangian for a spinless particle moving in a uniformly but not necessarily constantly accelerated reference frame; then, applying the strong equivalence principle (SEP) we obtain the Schroedinger equation for a particle in an inertial frame and in the presence of a uniform and constant gravity field. Second, using the associated Feynman propagator, we propagate an initial gaussian wave packet, with the final wave function and probability density depending on the ratio m/hbar, where m is the inertial mass of the particle, thus exhibiting the fact that the weak equivalence principle (WEP) is violated by quantum mechanics. Although due to rapid oscillations the wave function does not exist in the classical limit, the probability density is well defined and mass independent when hbar goes to 0, showing the recovery of the WEP. Finally, at the quantum level, a heavier particle does not necessarily falls faster than a lighter one; this depends on the relations between the initial and final common positions and times of the particles.

arXiv:quant-ph/0606172•Jun 20, 2006•4 citations

Generalized crossing states in the interacting case: The uniform gravitational field

Anthony Villanueva, Eric A. Galapon

We reconsider Baute et al.'s free crossing states [Phys. Rev. A 61, 022118 (2000)] and show that if we require a generalization in the interacting case that goes in complete parallel with the free-particle case, then this generalized crossing state cannot be arbitrary but is determined by the null space of the particle's quantum time-of-arrival operator. Nonetheless, the free crossing states appear as the leading term in the asymptotic expansion of our generalized crossing state in the limit of large momentum. We then examine the quantum time-of-arrival problem of a spinless particle in a uniform gravitational field. Mass-dependent time-of-arrival probability distributions emerge, signifying quantum departures from the weak equivalence principle. However, in the classical limit of large mass and vanishing uncertainty in position, the mass dependence of the quantum time-of-arrival distribution becomes exponentially small and the mean quantum time of arrival reduces to the classical time of arrival.

Physical Review A•Nov 29, 2010•5 citations
Abstract We study the effect of quantum statistics on the arrival time distribution of quantum particles computed through the probability current density. It is shown that symmetrization or asymmetrization of the wave function affects the arrival time distribution for even freely propagating particles. In order to investigate the effect of statistics on the weak equivalence principle in quantum mechanics (WEQ), we then compute the mean arrival time for wavepackets in free fall. The violation of WEQ through the effect of statistics on the mass dependence of the mean arrival time is clearly exhibited. We finally evaluate the effect of spin on the violation of WEQ using a different approach by including an explicit spin-dependence in the probability current distribution, and compare it with the approach using particle statistics. Our results show WEQ re-emerges smoothly in the limit of large mass.
Violation of the gravitational weak equivalence principle in quantum mechanics (WEQ) has been earlier studied using Gaussian wave packets in free fall.Here we study the effect of quantum statistics on the -Gaussian as well as non rrival time distribution of quantum particles computed through the probability current density.We show that a symmetrization or asymmetrization of the wave function impacts the arrival time distribution of wavepackets.The . the mass of the particles, and varies according to the statistics mean arrival time is dependent on
The weak equivalence principle of gravity is examined at the quantum level in two ways.First, the position detection probabilities of particles described by a non-Gaussian wave packet projected upwards against gravity around the classical turning point and also around the point of initial projection are calculated.These probabilities exhibit mass dependence at both these points, thereby reflecting the quantum violation of the weak equivalence principle.Second, the mean arrival time of freely falling particles is calculated using the quantum probability current, which also turns out to be mass dependent.Such a mass dependence is shown to be enhanced by increasing the non-Gaussianity parameter of the wave packet, thus signifying a stronger violation of the weak equivalence principle through a greater departure from Gaussianity of the initial wave packet.The mass dependence of both the position detection probabilities and the mean arrival time vanishes in the limit of large mass.Thus, compatibility between the weak equivalence principle and quantum mechanics is recovered in the macroscopic limit of the latter.A selection of Bohm trajectories is exhibited to illustrate these features in the free fall case.
The weak equivalence principle (WEP) in the quantum regime has been the subject of many studies with a broad range of approaches to the problem. Here, we tackle the problem anew through the time of arrival (TOA) operator approach. This is done by constructing the TOA operator for a nonrelativistic and structureless particle that is projected upward in a uniform gravitational field with an intended arrival point below the classical turning point. The TOA operator is constructed under the constraint that the inertial and gravitational masses are equivalent and that Galilean invariance is preserved. These constraints are implemented by Weyl quantization of the corresponding classical TOA function for the projectile. The expectation value of the TOA operator is explicitly shown to be equal to the classical time of arrival plus mass-dependent quantum correction terms, implying incompatibility of the WEP with quantum mechanics. The full extent of the violation of the WEP is shown through the mass dependence of TOA distribution for the projectile.
Investigation into the applicability of the equivalence principle in quantum mechanics has taken many forms, with varying conclusions. Here, a dynamical semiclassical description of a wave packet in terms of its center of mass and higher quantum fluctuations is applied to the case of a quantum particle in gravitational free fall. The analysis provides an intuitive account of the origin of mass dependence in quantum-gravitational dynamics through an effective potential that enforces the uncertainty principle. This potential has two implications: (i) The lowest order quantum fluctuations encoding the width and spreading of the wave packet obey an uncertainty relation whose observance is mass dependent. (ii) In an inhomogeneous gravitational field tidal effects couple the center of mass motion to the quantum fluctuations. The combined effect results in a clear demonstration of how some conceptions of the weak equivalence principle, based on mass dependence, are violated. The size of this violation is within sensitivities of current E\"otv\"os and clock-based return time experiments.
We use the Feynman path integral approach to nonrelativistic quantum mechanics twofold. First, we derive the lagrangian for a spinless particle moving in a uniformly but not necessarily constantly accelerated reference frame; then, applying the strong equivalence principle (SEP) we obtain the Schroedinger equation for a particle in an inertial frame and in the presence of a uniform and constant gravity field. Second, using the associated Feynman propagator, we propagate an initial gaussian wave packet, with the final wave function and probability density depending on the ratio m/hbar, where m is the inertial mass of the particle, thus exhibiting the fact that the weak equivalence principle (WEP) is violated by quantum mechanics. Although due to rapid oscillations the wave function does not exist in the classical limit, the probability density is well defined and mass independent when hbar goes to 0, showing the recovery of the WEP. Finally, at the quantum level, a heavier particle does not necessarily falls faster than a lighter one; this depends on the relations between the initial and final common positions and times of the particles.
We reconsider Baute et al.'s free crossing states [Phys. Rev. A 61, 022118 (2000)] and show that if we require a generalization in the interacting case that goes in complete parallel with the free-particle case, then this generalized crossing state cannot be arbitrary but is determined by the null space of the particle's quantum time-of-arrival operator. Nonetheless, the free crossing states appear as the leading term in the asymptotic expansion of our generalized crossing state in the limit of large momentum. We then examine the quantum time-of-arrival problem of a spinless particle in a uniform gravitational field. Mass-dependent time-of-arrival probability distributions emerge, signifying quantum departures from the weak equivalence principle. However, in the classical limit of large mass and vanishing uncertainty in position, the mass dependence of the quantum time-of-arrival distribution becomes exponentially small and the mean quantum time of arrival reduces to the classical time of arrival.