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

Revista Mexicana de Física E

The free fall in three Physics theories

Edgar Luis Luna Hernández, Jorge Alejandro Bernal Arroyo, Luis Enrique Ramón Pedrero

Published Jan 19, 2024• 0 citations
Publisher

Abstract

This paper explores the interplay between Classical Mechanics, Relativistic Mechanics, and Quantum Mechanics through an analysis of the free fall phenomenon. We investigate the probability density functions and corresponding plots in each theory, alongside calculating the expected values of position and momentum. By observing the behavior of these results as they approach the classical limit, we confirm the hypothesis that these theories can be connected through their probability density functions. Furthermore, we discuss the validity of the correspondence principle in Quantum Mechanics, while also examining, in a non-rigorous manner, the validity of the weak equivalence principle within each of the aforementioned theories.

DOI
10.31349/revmexfise.21.010214

Related papers

On the Classical Limit of Freely Falling Quantum Particles, Quantum Corrections and the Emergence of the Equivalence Principle

Juan A. Cañas, J. Bernal, A. Martín-Ruiz

Quantum and classical mechanics are fundamentally different theories, but the correspondence principle states that quantum particles behave classically in the appropriate limit. For high-energy periodic quantum systems, the emergence of the classical description should be understood in a distributional sense, i.e., the quantum probability density approaches the classical distribution when the former is coarse-grained. Following a simple reformulation of this limit in the Fourier space, in this paper, we investigate the macroscopic behavior of freely falling quantum particles. To illustrate how the method works and to fix some ideas, we first successfully apply it to the case of a particle in a box. Next, we show that, for a particle bouncing under the gravity field, in the limit of a high quantum number, the leading term of the quantum distribution corresponds to the exact classical distribution plus sub-leading corrections, which we interpret as quantum corrections at the macroscopic level.

Universe•Sep 2, 2024•2 citations

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.

•Jan 1, 1997•5 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

Quantum Mechanics as a Classical Theory I: Non-relativistic Theory

L. S. F. Olavo

The objective of this series of three papers is to axiomatically derive quantum mechanics from classical mechanics and two other basic axioms. In this first paper, Schreodinger's equation for the density matrix is fist obtained and from it Schroedinger's equation for the wave functions is derived. The momentum and position operators acting upon the density matrix are defined and it is then demonstrated that they commute. Pauli's equation for the density matrix is also obtained. A statistical potential formally identical to the quantum potential of Bohm's hidden variable theory is introduced, and this quantum potential is reinterpreted through the formalism here proposed. It is shown that, for dispersion free {\it ensembles% }, Schroedinger's equation for the density matrix is equivalent to Newton's equations. A general non-ambiguous procedure for the construction of operators which act upon the density matrix is presented. It is also shown how these operators can be reduced to those which act upon the wave functions.

arXiv:quant-ph/9503020•Mar 28, 1995•3 citations

Emergent universality of free fall from quantum mechanics

Juan A. Cañas, A. Martín-Ruiz, J. Bernal

Classical and quantum mechanical descriptions of motion are fundamentally different. The Universality of Free Fall (UFF) is a distinguishing feature of the classical motion (which has been verified with astonishing precision), while quantum theory tell us only about probabilities and uncertainties thus breaking the UFF. There are strong reasons to believe that the classical description must emerge, under plausible hypothesis, from quantum mechanics. In this paper, we show that the UFF is an emergent phenomenon: the coarse-grained quantum distribution for high-energy levels leads to the classical distribution as the lowest order plus quantum corrections. We estimate the size of these corrections on the Eötvös parameter and discuss the physical implications.

arXiv:2405.07403•International Journal of Modern Physics D•Jun 29, 2024•1 citation
This paper explores the interplay between Classical Mechanics, Relativistic Mechanics, and Quantum Mechanics through an analysis of the free fall phenomenon. We investigate the probability density functions and corresponding plots in each theory, alongside calculating the expected values of position and momentum. By observing the behavior of these results as they approach the classical limit, we confirm the hypothesis that these theories can be connected through their probability density functions. Furthermore, we discuss the validity of the correspondence principle in Quantum Mechanics, while also examining, in a non-rigorous manner, the validity of the weak equivalence principle within each of the aforementioned theories.
Quantum and classical mechanics are fundamentally different theories, but the correspondence principle states that quantum particles behave classically in the appropriate limit. For high-energy periodic quantum systems, the emergence of the classical description should be understood in a distributional sense, i.e., the quantum probability density approaches the classical distribution when the former is coarse-grained. Following a simple reformulation of this limit in the Fourier space, in this paper, we investigate the macroscopic behavior of freely falling quantum particles. To illustrate how the method works and to fix some ideas, we first successfully apply it to the case of a particle in a box. Next, we show that, for a particle bouncing under the gravity field, in the limit of a high quantum number, the leading term of the quantum distribution corresponds to the exact classical distribution plus sub-leading corrections, which we interpret as quantum corrections at the macroscopic level.
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.
The objective of this series of three papers is to axiomatically derive quantum mechanics from classical mechanics and two other basic axioms. In this first paper, Schreodinger's equation for the density matrix is fist obtained and from it Schroedinger's equation for the wave functions is derived. The momentum and position operators acting upon the density matrix are defined and it is then demonstrated that they commute. Pauli's equation for the density matrix is also obtained. A statistical potential formally identical to the quantum potential of Bohm's hidden variable theory is introduced, and this quantum potential is reinterpreted through the formalism here proposed. It is shown that, for dispersion free {\it ensembles% }, Schroedinger's equation for the density matrix is equivalent to Newton's equations. A general non-ambiguous procedure for the construction of operators which act upon the density matrix is presented. It is also shown how these operators can be reduced to those which act upon the wave functions.
Classical and quantum mechanical descriptions of motion are fundamentally different. The Universality of Free Fall (UFF) is a distinguishing feature of the classical motion (which has been verified with astonishing precision), while quantum theory tell us only about probabilities and uncertainties thus breaking the UFF. There are strong reasons to believe that the classical description must emerge, under plausible hypothesis, from quantum mechanics. In this paper, we show that the UFF is an emergent phenomenon: the coarse-grained quantum distribution for high-energy levels leads to the classical distribution as the lowest order plus quantum corrections. We estimate the size of these corrections on the Eötvös parameter and discuss the physical implications.