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:2203.01787 · Physical Review A

Testing gravitational self-interaction via matter-wave interferometry

Sourav Kesharee Sahoo, Ashutosh Dash, Radhika Vathsan, Tabish Qureshi

Published Jul 21, 2022• 2 citations
arXivHTMLPDF

Abstract

The Schr\"odinger-Newton equation has frequently been studied as a nonlinear modification of the Schr\"odinger equation incorporating gravitational self-interaction. However, there is no evidence yet as to whether nature actually behaves this way. This work investigates a possible way to experimentally test gravitational self-interaction. The effect of self-gravity on the interference of massive particles is studied by numerically solving the Schr\"odinger-Newton equation for a particle passing through a double-slit. The results show that the presence of gravitational self-interaction has an effect on the fringe width of the interference that can be tested in matter-wave interferometry experiments. Notably, this approach can distinguish between gravitational self-interaction and environment-induced decoherence, as the latter does not affect the fringe width. This result will also provide a way to test if gravity requires to be quantized on the scale of ordinary quantum mechanics.

DOI
10.1103/physreva.106.012215

Related papers

Newtonian self-gravity in trapped quantum systems and experimental tests

André Großardt

No experimental evidence exists, to date, whether or not the gravitational field must be quantised. Theoretical arguments in favour of quantisation are inconclusive. The most straightforward alternative to quantum gravity, a coupling between classical gravity and quantum matter according to the semi-classical Einstein equations, yields a nonlinear modification of the Schrödinger equation. Here, effects of this so-called Schrödinger-Newton equation are discussed, which allow for technologically feasible experimental tests.

arXiv:1702.04309•Journal of Physics Conference Series•Aug 1, 2017•0 citations

State-Dependent Gravitational Self-Interaction in Mesoscopic Quantum Superpositions ✔ Precise, conservative, reviewer-safe ✔ Matches the PDF content exactly ✔ Ideal for Zenodo + later journal submission

Morris, Jamie

This work presents numerical and theoretical evidence for a testable regime in which semiclassical Schrödinger–Newton dynamics predict a state-dependent gravitational self-interaction in mesoscopic quantum systems. Using large-scale Split-Step Fourier Method (SSFM) simulations, we identify a mass window (≈10⁻¹¹–10⁻¹⁰ kg) where quantum coherence and gravitational self-interaction coexist without immediate decoherence. In this regime, the gravitational self-energy depends smoothly on the spatial structure of the quantum state, leading to a differential phase evolution between superposition states with identical external potentials but different mass-density distributions. The predicted phase signal scales as m² and reaches experimentally relevant magnitudes (Δφ ≈ 10⁻³ rad) for millisecond evolution times, making the effect accessible to next-generation matter-wave and optomechanical interferometry. The work systematically validates the numerical approach, demonstrates energy conservation and convergence of the nonlinear dynamics, identifies a stable “breathing-mode” regime near 10⁻¹⁰ kg, and isolates the gravitational origin of the effect via null tests with the Schrödinger–Newton term removed. This preprint makes no claim regarding spacetime engineering, geometry manipulation, or violations of the equivalence principle. It is explicitly framed as a falsifiable test of semiclassical gravity in a previously inaccessible experimental regime. Confirmation or null detection would provide strong constraints on Schrödinger–Newton–type models and inform the ongoing search for the correct quantum–gravity interface.

•Dec 15, 2025•0 citations

Dephasing and inhibition of spin interference from semi-classical self-gravitation

André Großardt

Abstract We present a detailed derivation of a model to study effects of self-gravitation from semi-classical gravity, described by the Schrödinger–Newton equation, employing spin superposition states in inhomogeneous magnetic fields, as proposed recently for experiments searching for gravity induced entanglement. Approximations for the experimentally relevant limits are discussed. Results suggest that spin interferometry could provide a more accessible route towards an experimental test of quantum aspects of gravity than both previous proposals to test semi-classical gravity and the observation of gravitational spin entanglement.

arXiv:2107.05985•Classical and Quantum Gravity•Nov 4, 2021•5 citations

Self-gravitating interferometry and intrinsic decoherence

Cisco Gooding, William George Unruh

To investigate the possibility that intrinsic gravitational decoherence can be theoretically demonstrated within canonical quantum gravity, we develop a model of a self-gravitating interferometer. We search for evidence in the resulting interference pattern that would indicate coherence is fundamentally limited due to general relativistic effects. To eliminate the occurrence of gravitational waves, we work in spherical symmetry, and construct the ``beam'' of the interferometer out of WKB states for an infinitesimally thin shell of matter. For internal consistency, we encode information about the beam optics within the dynamics of the shell itself, by arranging an ideal fluid on the surface of the shell with an equation of state that enforces beam splitting and reflections. We then determine sufficient conditions for (interferometric) coherence to be fully present even after general relativistic corrections are introduced, test whether or not they can be satisfied, and remark on the implications of the results.

arXiv:1407.7149•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Aug 27, 2014•16 citations

Gravitational self-localization for spherical masses

M. Jääskeläinen

In this work, I consider the center-of-mass wave function for a homogenous sphere under the influence of the self-interaction due to Newtonian gravity. I solve for the ground state numerically and calculate the average radius as a measure of its size. For small masses, $M\ensuremath{\lesssim}{10}^{\ensuremath{-}17}$ kg, the radial size is independent of density, and the ground state extends beyond the extent of the sphere. For masses larger than this, the ground state is contained within the sphere and to a good approximation given by the solution for an effective radial harmonic-oscillator potential. This work thus determines the limits of applicability of the point-mass Newton Schr\"odinger equations for spherical masses. In addition, I calculate the fringe visibility for matter-wave interferometry and find that in the low-mass case, interferometry can in principle be performed, whereas for the latter case, it becomes impossible. Based on this, I discuss this transition as a possible boundary for the quantum-classical crossover, independent of the usually evoked environmental decoherence. The two regimes meet at sphere sizes $R\ensuremath{\approx}{10}^{\ensuremath{-}7}$ m, and the density of the material causes only minor variations in this value.

Physical Review A•Nov 8, 2012•8 citations

Effects of Newtonian gravitational self-interaction in harmonically trapped quantum systems

André Großardt, James Bateman, Hendrik Ulbricht +1 more

The Schrödinger-Newton equation has gained attention in the recent past as a nonlinear modification of the Schrödinger equation due to a gravitational self-interaction. Such a modification is expected from a fundamentally semi-classical theory of gravity and can, therefore, be considered a test case for the necessity of the quantisation of the gravitational field. Here we provide a thorough study of the effects of the Schrödinger-Newton equation for a micron-sized sphere trapped in a harmonic oscillator potential. We discuss both the effect on the energy eigenstates and the dynamical behaviour of squeezed states, covering the experimentally relevant parameter regimes.

arXiv:1510.01262•Scientific Reports•Aug 4, 2016•20 citations
The Schr"odinger-Newton equation has frequently been studied as a nonlinear modification of the Schr"odinger equation incorporating gravitational self-interaction. However, there is no evidence yet as to whether nature actually behaves this way. This work investigates a possible way to experimentally test gravitational self-interaction. The effect of self-gravity on the interference of massive particles is studied by numerically solving the Schr"odinger-Newton equation for a particle passing through a double-slit. The results show that the presence of gravitational self-interaction has an effect on the fringe width of the interference that can be tested in matter-wave interferometry experiments. Notably, this approach can distinguish between gravitational self-interaction and environment-induced decoherence, as the latter does not affect the fringe width. This result will also provide a way to test if gravity requires to be quantized on the scale of ordinary quantum mechanics.
No experimental evidence exists, to date, whether or not the gravitational field must be quantised. Theoretical arguments in favour of quantisation are inconclusive. The most straightforward alternative to quantum gravity, a coupling between classical gravity and quantum matter according to the semi-classical Einstein equations, yields a nonlinear modification of the Schrödinger equation. Here, effects of this so-called Schrödinger-Newton equation are discussed, which allow for technologically feasible experimental tests.
This work presents numerical and theoretical evidence for a testable regime in which semiclassical Schrödinger–Newton dynamics predict a state-dependent gravitational self-interaction in mesoscopic quantum systems. Using large-scale Split-Step Fourier Method (SSFM) simulations, we identify a mass window (≈10⁻¹¹–10⁻¹⁰ kg) where quantum coherence and gravitational self-interaction coexist without immediate decoherence. In this regime, the gravitational self-energy depends smoothly on the spatial structure of the quantum state, leading to a differential phase evolution between superposition states with identical external potentials but different mass-density distributions. The predicted phase signal scales as m² and reaches experimentally relevant magnitudes (Δφ ≈ 10⁻³ rad) for millisecond evolution times, making the effect accessible to next-generation matter-wave and optomechanical interferometry. The work systematically validates the numerical approach, demonstrates energy conservation and convergence of the nonlinear dynamics, identifies a stable “breathing-mode” regime near 10⁻¹⁰ kg, and isolates the gravitational origin of the effect via null tests with the Schrödinger–Newton term removed. This preprint makes no claim regarding spacetime engineering, geometry manipulation, or violations of the equivalence principle. It is explicitly framed as a falsifiable test of semiclassical gravity in a previously inaccessible experimental regime. Confirmation or null detection would provide strong constraints on Schrödinger–Newton–type models and inform the ongoing search for the correct quantum–gravity interface.
Abstract We present a detailed derivation of a model to study effects of self-gravitation from semi-classical gravity, described by the Schrödinger–Newton equation, employing spin superposition states in inhomogeneous magnetic fields, as proposed recently for experiments searching for gravity induced entanglement. Approximations for the experimentally relevant limits are discussed. Results suggest that spin interferometry could provide a more accessible route towards an experimental test of quantum aspects of gravity than both previous proposals to test semi-classical gravity and the observation of gravitational spin entanglement.
To investigate the possibility that intrinsic gravitational decoherence can be theoretically demonstrated within canonical quantum gravity, we develop a model of a self-gravitating interferometer. We search for evidence in the resulting interference pattern that would indicate coherence is fundamentally limited due to general relativistic effects. To eliminate the occurrence of gravitational waves, we work in spherical symmetry, and construct the ``beam'' of the interferometer out of WKB states for an infinitesimally thin shell of matter. For internal consistency, we encode information about the beam optics within the dynamics of the shell itself, by arranging an ideal fluid on the surface of the shell with an equation of state that enforces beam splitting and reflections. We then determine sufficient conditions for (interferometric) coherence to be fully present even after general relativistic corrections are introduced, test whether or not they can be satisfied, and remark on the implications of the results.
In this work, I consider the center-of-mass wave function for a homogenous sphere under the influence of the self-interaction due to Newtonian gravity. I solve for the ground state numerically and calculate the average radius as a measure of its size. For small masses, $M\ensuremath{\lesssim}{10}^{\ensuremath{-}17}$ kg, the radial size is independent of density, and the ground state extends beyond the extent of the sphere. For masses larger than this, the ground state is contained within the sphere and to a good approximation given by the solution for an effective radial harmonic-oscillator potential. This work thus determines the limits of applicability of the point-mass Newton Schr\"odinger equations for spherical masses. In addition, I calculate the fringe visibility for matter-wave interferometry and find that in the low-mass case, interferometry can in principle be performed, whereas for the latter case, it becomes impossible. Based on this, I discuss this transition as a possible boundary for the quantum-classical crossover, independent of the usually evoked environmental decoherence. The two regimes meet at sphere sizes $R\ensuremath{\approx}{10}^{\ensuremath{-}7}$ m, and the density of the material causes only minor variations in this value.
The Schrödinger-Newton equation has gained attention in the recent past as a nonlinear modification of the Schrödinger equation due to a gravitational self-interaction. Such a modification is expected from a fundamentally semi-classical theory of gravity and can, therefore, be considered a test case for the necessity of the quantisation of the gravitational field. Here we provide a thorough study of the effects of the Schrödinger-Newton equation for a micron-sized sphere trapped in a harmonic oscillator potential. We discuss both the effect on the energy eigenstates and the dynamical behaviour of squeezed states, covering the experimentally relevant parameter regimes.