On quantum gravity tests with composite particles

Models of quantum gravity imply a fundamental revision of our description of position and momentum that manifests in modifications of the canonical commutation relations. Experimental tests of such modifications remain an outstanding challenge. These corrections scale with the mass of test particles, which motivates experiments using macroscopic composite particles. Here we consider a challenge to such tests, namely that quantum gravity corrections of canonical commutation relations are expected to be suppressed with increasing number of constituent particles. Since the precise scaling of this suppression is unknown, it needs to be bounded experimentally and explicitly incorporated into rigorous analyses of quantum gravity tests. We analyse this scaling based on data from past experiments involving macroscopic pendula, and provide tight bounds that exceed those of current experiments based on quantum mechanical oscillators. Furthermore, we discuss possible experiments that promise even stronger bounds thus bringing rigorous and well-controlled tests of quantum gravity closer to reality.Models of quantum gravity imply a fundamental revision of our description of position and momentum that manifests in modifications of the canonical commutation relations. Experimental tests of such modifications remain an outstanding challenge. These corrections scale with the mass of test particles, which motivates experiments using macroscopic composite particles. Here we consider a challenge to such tests, namely that quantum gravity corrections of canonical commutation relations are expected to be suppressed with increasing number of constituent particles. Since the precise scaling of this suppression is unknown, it needs to be bounded experimentally and explicitly incorporated into rigorous analyses of quantum gravity tests. We analyse this scaling based on data from past experiments involving macroscopic pendula, and provide tight bounds that exceed those of current experiments based on quantum mechanical oscillators. Furthermore, we discuss possible experiments that promise even stronger bounds thus bringing rigorous and well-controlled tests of quantum gravity closer to reality.

arXiv:1908.11164Nature CommunicationsAug 6, 202045 citations

Probing quantum gravity effects with quantum mechanical oscillators

M. Bonaldi, A. Borrielli, Avishek Chowdhury +13 more

Abstract Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that account for a minimal scale length, yield a dynamics that can be codified in additional Hamiltonian terms. When applied to the paradigmatic case of a mechanical oscillator, such terms, at the lowest order in the deformation parameter, introduce a weak intrinsic nonlinearity and, consequently, deviations from the classical trajectory. This point of view has stimulated several experimental proposals and realizations, leading to meaningful upper limits to the deformation parameter. All such experiments are based on classical mechanical oscillators, i.e., excited from a thermal state. We remark indeed that decoherence, that plays a major role in distinguishing the classical from the quantum behavior of (macroscopic) systems, is not usually included in phenomenological quantum gravity models. However, it would not be surprising if peculiar features that are predicted by considering the joined roles of gravity and quantum physics should manifest themselves just on purely quantum objects. On the basis of this consideration, we propose experiments aiming to observe possible quantum gravity effects on macroscopic mechanical oscillators that are preliminary prepared in a high purity state, and we report on the status of their realization. Graphical abstractAbstract Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that account for a minimal scale length, yield a dynamics that can be codified in additional Hamiltonian terms. When applied to the paradigmatic case of a mechanical oscillator, such terms, at the lowest order in the deformation parameter, introduce a weak intrinsic nonlinearity and, consequently, deviations from the classical trajectory. This point of view has stimulated several experimental proposals and realizations, leading to meaningful upper limits to the deformation parameter. All such experiments are based on classical mechanical oscillators, i.e., excited from a thermal state. We remark indeed that decoherence, that plays a major role in distinguishing the classical from the quantum behavior of (macroscopic) systems, is not usually included in phenomenological quantum gravity models. However, it would not be surprising if peculiar features that are predicted by considering the joined roles of gravity and quantum physics should manifest themselves just on purely quantum objects. On the basis of this consideration, we propose experiments aiming to observe possible quantum gravity effects on macroscopic mechanical oscillators that are preliminary prepared in a high purity state, and we report on the status of their realization. Graphical abstract

arXiv:2004.14371The European Physical Journal DSep 1, 202018 citations

Testing quantum gravity by nanodiamond interferometry with nitrogen-vacancy centers

Andreas Albrecht, Alex Retzker, Martin Bodo Plenio

Interferometry with massive particles may have the potential to explore the limitations of standard quantum mechanics, in particular where it concerns its boundary with general relativity and the yet to be developed theory of quantum gravity. This development is hindered considerably by the lack of experimental evidence and testable predictions. Analyzing effects that appear to be common to many of such theories, such as a modification of the energy dispersion and of the canonical commutation relation within the standard framework of quantum mechanics, has been proposed as a possible way forward. Here we analyze in some detail the impact of a modified energy-momentum dispersion in a Ramsey-Bord\'e setup and provide achievable bounds of these correcting terms when operating such an interferometer with nanodiamonds. Thus, taking thermal and gravitational disturbances into account will show that without specific prerequisites, quantum gravity modifications may in general be suppressed requiring a revision of previously estimated bounds. As a possible solution we propose a stable setup which is rather insensitive to these effects. Finally, we address the problems of decoherence and pulse errors in such setups and discuss the scalings and advantages with increasing particle mass.Interferometry with massive particles may have the potential to explore the limitations of standard quantum mechanics, in particular where it concerns its boundary with general relativity and the yet to be developed theory of quantum gravity. This development is hindered considerably by the lack of experimental evidence and testable predictions. Analyzing effects that appear to be common to many of such theories, such as a modification of the energy dispersion and of the canonical commutation relation within the standard framework of quantum mechanics, has been proposed as a possible way forward. Here we analyze in some detail the impact of a modified energy-momentum dispersion in a Ramsey-Bord\'e setup and provide achievable bounds of these correcting terms when operating such an interferometer with nanodiamonds. Thus, taking thermal and gravitational disturbances into account will show that without specific prerequisites, quantum gravity modifications may in general be suppressed requiring a revision of previously estimated bounds. As a possible solution we propose a stable setup which is rather insensitive to these effects. Finally, we address the problems of decoherence and pulse errors in such setups and discuss the scalings and advantages with increasing particle mass.

arXiv:1403.6038Physical Review ASep 22, 201464 citations

Probing Quantum Gravity with Large Molecular Wave-packets

Carlos Villalpando, Sujoy K. Modak

The most obvious obstacle behind a direct test of Quantum Gravity (QG) is its energy scale ( $10^{19}$ GeV), which remains well outside of any human made machine. The next best possible approach is to provide indirect tests on effective theories of QG which can be performed in a lower energy scale. This paper is aimed in this direction, and shows a promising path to test the existence of the fundamental minimal length scale of Nature by measuring the dispersion of free, large molecular wave-packets. The existence of the minimal length is believed to be the reason for a modified commutation relationship between the position and momentum operators and, in this paper, we show that such a modification of the commutator has a profound effect on the dispersion rate of free wave-packets, and precise measurement on the broadening times of large molecular wave-packets (such as $C_{60}$ , $C_{176}$ and large organic molecules) provide a promising path for an indirect test of quantum gravity, in a laboratory setting.The most obvious obstacle behind a direct test of Quantum Gravity (QG) is its energy scale ($10^{19}$ GeV), which remains well outside of any human made machine. The next best possible approach is to provide indirect tests on effective theories of QG which can be performed in a lower energy scale. This paper is aimed in this direction, and shows a promising path to test the existence of the fundamental minimal length scale of Nature by measuring the dispersion of free, large molecular wave-packets. The existence of the minimal length is believed to be the reason for a modified commutation relationship between the position and momentum operators and, in this paper, we show that such a modification of the commutator has a profound effect on the dispersion rate of free wave-packets, and precise measurement on the broadening times of large molecular wave-packets (such as $C_{60}$, $C_{176}$ and large organic molecules) provide a promising path for an indirect test of quantum gravity, in a laboratory setting.

APS April Meeting AbstractsJan 1, 20191 citation

A Spin-Based Pathway to Testing the Quantum Nature of Gravity

Sougato Bose, Anupam Mazumdar, Roger Penrose +52 more

A key open problem in physics is the correct way to combine gravity (described by general relativity) with everything else (described by quantum mechanics). This problem suggests that general relativity and possibly also quantum mechanics need fundamental corrections. Most physicists expect that gravity should be quantum in character, but gravity is fundamentally different to the other forces because it alone is described by spacetime geometry. Experiments are needed to test whether gravity, and hence space-time, is quantum or classical. We propose an experiment to test the quantum nature of gravity by checking whether gravity can entangle two micron-sized crystals. A pathway to this is to create macroscopic quantum superpositions of each crystal first using embedded spins and Stern-Gerlach forces. These crystals could be nanodiamonds containing nitrogen-vacancy (NV) centres. The spins can subsequently be measured to witness the gravitationally generated entanglement. This is based on extensive theoretical feasibility studies and experimental progress in quantum technology. The eventual experiment will require a medium-sized consortium with excellent suppression of decoherence including vibrations and gravitational noise. In this white paper, we review the progress and plans towards realizing this. While implementing these plans, we will further explore the most macroscopic superpositions that are possible, which will test theories that predict a limit to this.A key open problem in physics is the correct way to combine gravity (described by general relativity) with everything else (described by quantum mechanics). This problem suggests that general relativity and possibly also quantum mechanics need fundamental corrections. Most physicists expect that gravity should be quantum in character, but gravity is fundamentally different to the other forces because it alone is described by spacetime geometry. Experiments are needed to test whether gravity, and hence space-time, is quantum or classical. We propose an experiment to test the quantum nature of gravity by checking whether gravity can entangle two micron-sized crystals. A pathway to this is to create macroscopic quantum superpositions of each crystal first using embedded spins and Stern-Gerlach forces. These crystals could be nanodiamonds containing nitrogen-vacancy (NV) centres. The spins can subsequently be measured to witness the gravitationally generated entanglement. This is based on extensive theoretical feasibility studies and experimental progress in quantum technology. The eventual experiment will require a medium-sized consortium with excellent suppression of decoherence including vibrations and gravitational noise. In this white paper, we review the progress and plans towards realizing this. While implementing these plans, we will further explore the most macroscopic superpositions that are possible, which will test theories that predict a limit to this.

arXiv:2509.01586Sep 1, 20251 citation

Lamb shift of rotational energy levels in quantum gravity

Oliver Benz, Marius Krumm, Wolfgang Wieland

One of the major challenges of modern foundational physics is the combination of quantum physics and general relativity into a theory of quantum gravity. A severe obstacle are the required extremely high energy scales for direct tests of quantum gravity effects. In recent years, attention has shifted towards near-future experimental predictions of effective or phenomenological models, such as gravitationally induced entanglement or interactions of linearized gravity with non-relativistic measurement devices. These developments motivate us to study the coupling between the quantized metric perturbation and an anisotropic quantum rigid rotor. The intuitive motivation for our study is that a sufficiently heavy rotor consists of a very large number of component systems. Although quantum gravitational effects are completely negligible at the scale of a single atom or molecule, the effects can get amplified by the sheer number of constituents. The resulting effective model describes the gravitational analogue of the angulon quasiparticle excitations discussed in condensed matter physics, suggesting a pathway for future analogue experiments. As a first concrete test of our model, we derive the gravitational Lamb shift for the energy eigenstates of the rotor, which become dressed by a cloud of virtual gravitons. Although the effect is very small, it could provide a concrete test for whether gravity is truly quantum.One of the major challenges of modern foundational physics is the combination of quantum physics and general relativity into a theory of quantum gravity. A severe obstacle are the required extremely high energy scales for direct tests of quantum gravity effects. In recent years, attention has shifted towards near-future experimental predictions of effective or phenomenological models, such as gravitationally induced entanglement or interactions of linearized gravity with non-relativistic measurement devices. These developments motivate us to study the coupling between the quantized metric perturbation and an anisotropic quantum rigid rotor. The intuitive motivation for our study is that a sufficiently heavy rotor consists of a very large number of component systems. Although quantum gravitational effects are completely negligible at the scale of a single atom or molecule, the effects can get amplified by the sheer number of constituents. The resulting effective model describes the gravitational analogue of the angulon quasiparticle excitations discussed in condensed matter physics, suggesting a pathway for future analogue experiments. As a first concrete test of our model, we derive the gravitational Lamb shift for the energy eigenstates of the rotor, which become dressed by a cloud of virtual gravitons. Although the effect is very small, it could provide a concrete test for whether gravity is truly quantum.

gr-qcCross-listedarXiv:2610.28754Oct 22, 2026

The most obvious obstacle behind a direct test of Quantum Gravity (QG) is its energy scale (

10^{19}

GeV), which remains well outside of any human made machine. The next best possible approach is to provide indirect tests on effective theories of QG which can be performed in a lower energy scale. This paper is aimed in this direction, and shows a promising path to test the existence of the fundamental minimal length scale of Nature by measuring the dispersion of free, large molecular wave-packets. The existence of the minimal length is believed to be the reason for a modified commutation relationship between the position and momentum operators and, in this paper, we show that such a modification of the commutator has a profound effect on the dispersion rate of free wave-packets, and precise measurement on the broadening times of large molecular wave-packets (such as

C_{60}

C_{176}

and large organic molecules) provide a promising path for an indirect test of quantum gravity, in a laboratory setting.