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arXiv:2602.12266 · Physical Review A

Repulsive Gravitational Force as a Witness of the Quantum Nature of Gravity

Pablo L. Saldanha, Chiara Marletto, Vlatko Vedral

quant-phgr-qcSubmitted Feb 12, 2026• Announced Feb 13, 2026• 1 citation• Revised Jul 20, 2026 (v2)
v1 · Feb 12, 2026v2 · Jul 20, 2026
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Abstract

We show that a single spatially superposed 'source' mass acting on a 'probe' matter wavepacket can reveal the quantum nature of the gravitational field. For this we use a specific state preparation and measurement of the superposed source mass, including a postselection, which altogether results in a repulsive gravitational force on the probe particle. A classical gravitational field can never lead to repulsion, as the effect requires quantum interference of two distinct states of gravity. The eventual observation of such an effect would be a violation of Einstein's theory of general relativity, where gravity is always attractive. We also present a calculation in the Heisenberg picture under the formalism of weak values that illustrates how repulsion is achieved. Finally, we estimate the range of parameters (masses and the spatio-temporal extent of interference) for which the experiment is feasible.

Comments
5 pages, 2 figures. v2: Discussions were improved. Minor errors were fixed

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We show that a single spatially superposed 'source' mass acting on a 'probe' matter wavepacket can reveal the quantum nature of the gravitational field. For this we use a specific state preparation and measurement of the superposed source mass, including a postselection, which altogether results in a repulsive gravitational force on the probe particle. A classical gravitational field can never lead to repulsion, as the effect requires quantum interference of two distinct states of gravity. The eventual observation of such an effect would be a violation of Einstein's theory of general relativity, where gravity is always attractive. We also present a calculation in the Heisenberg picture under the formalism of weak values that illustrates how repulsion is achieved. Finally, we estimate the range of parameters (masses and the spatio-temporal extent of interference) for which the experiment is feasible.
A classic feature of gravity is that it is an attractive force. If a source mass is prepared in a localized (classical- like) state, it will cause another probe mass to move towards it. Here we consider the situation in which a source mass is prepared in a quantum superposition of distinct spatial states while a probe mass interacts with it. Conditional on the detection of the source mass in a specific state, the probe mass will be found to move away from the source mass (repulsion). This signifies the quantum superposition of gravitational forces acting on the probe mass and thereby the fact that spacetime can exist in quantum superpositions. The technique used is the repulsive effect arising from an anomalous negative weak value. A potential experimental implementation with spin bearing nanocrystals is outlined.
Experiments are beginning to probe the interaction of quantum particles with gravitational fields beyond the uniform-field regime. In nonrelativistic quantum mechanics, the gravitational field in such experiments can be written as a superposition state. We empirically demonstrate that semiclassical theories of gravity can avoid gravitational superposition states only by decoupling the gravitational field energy from the quantum particle's time evolution. Furthermore, such theories must specify a preferred quantum reference frame in which the equations of motion are valid. To the extent that these properties are theoretically implausible, recent experiments provide indirect evidence that gravity has quantum features. Proposed experiments with superposed gravitational sources would provide even stronger evidence that gravity is nonclassical.
We address the problem of estimating the mass of a (quantum) particle interacting with a classical gravitational field. In particular, we analyze in details the ultimate bounds to precision imposed by quantum mechanics and study the effects of gravity in a variety of settings. Our results show that the presence of a gravitational field generally leads to a precision gain, which can be significant in a regime half-way between the quantum and classical domains. We also address quantum enhancement to precision, i.e. the advantages coming from taking into account the quantum nature of the probe particle, and show that non-classicality is indeed a relevant resource for mass estimation. In particular, we suggest schemes for mass-sensing measurements using quantum probes and show that upon employing non-classical states like quantum coherent superpositions one may improve precisions by orders of magnitude. In addition, we discuss the compatibility of the weak equivalence principle (WEP) within the quantum regime using as a guide the notion of Fisher Information. We find that the information on the probe's mass that can be extracted through position measurements is unchanged by turning on a uniform gravitational field. This conclusion is somehow at variance with certain views expressed in the literature that the WEP cannot hold in the quantum regime. In fact, our results show that in an information-theoretic framework, no clash occurs between quantum mechanics and the WEP.
Aspects of quantum limits for the detection of a classical force The development of the theory of QND measurements was triggered by the problem of detecting a small classical force that acts on a quantum probe―e.g. on a free mass or an oscillator, see the review article and the monograph. This problem arose most especially in gravitational-wave experiments. Astrophysical estimates indicate that the gravitational waves from cosmic sources should be so strong that they behave almost perfectly classically. During the measuring time the number of gravitons that pass within one wavelength of the measuring device is enormously larger than unity; and correspondingly, as would be the case if the waves were electromagnetic, quantum effects in the radiation are utterly negligible. A central feature of gravitational waves is their extremely weak interaction with matter. Because of this weakness, the response of the measuring device's probe object to the waves is so small that it may be comparable to the object's quantum mechanical uncertainties. At the same time, the weakness of the interaction guarantees that there is almost no back action of the probe on the gravitational-wave field. As a result, the gravitational wave acts on the probe as through it were a precisely classical force (i.e. a force that is independent of the probe's quantum state).
Quantum mechanics and general relativity have been extensively and independently confirmed in many experiments. However, the interplay of the two theories has never been tested: all experiments that measured the influence of gravity on quantum systems are consistent with non-relativistic, Newtonian gravity. On the other hand, all tests of general relativity can be described within the framework of classical physics. Here we discuss a quantum interference experiment with single photons that can probe quantum mechanics in curved space-time. We consider a single photon traveling in superposition along two paths in an interferometer, with each arm experiencing a different gravitational time dilation. If the difference in the time dilations is comparable with the photon's coherence time, the visibility of the quantum interference is predicted to drop, while for shorter time dilations the effect of gravity will result only in a relative phase shift between the two arms. We discuss what aspects of the interplay between quantum mechanics and general relativity are probed in such experiments and analyze the experimental feasibility.
The quantum nature of gravity is one of physics' greatest unsolved problems, with existing experimental proposals facing formidable challenges in maintaining spatial superpositions of massive objects against decoherence. We propose a fundamentally different approach that bypasses these difficulties. The central insight is that a quantum gravitational field can imprint a gauge-invariant phase on a particle's wavefunction even along an open trajectory, arising from the quantum backreaction of the source. This phase, which manifests prior to the final recombination stage of an interferometer and cannot be generated by a classical gravitational field, provides an operationally direct witness to the quantumness of gravity. Our experimental design uses a single photon whose accumulated gravitational phase due to the Earth is transferred via absorption to auxiliary atoms near the end of the interferometer sequence, preserving the open-path character essential for the test. We scale the interferometer to yield a detectable phase of order 10−310^{-3}10−3 rad and show how non-local correlation measurements on the atoms can access this gauge-invariant signature. Leveraging established quantum optical and atomic techniques, this proposal offers a feasible path to distinguish quantum from classical gravity. A positive result would provide the first experimental evidence for the quantum nature of gravitational fields, with profound implications for quantum gravity theories.