On tests of the quantum nature of gravitational interactions in presence of non-linear corrections to quantum mechanics

Giovanni Spaventa1, Ludovico Lami1,2,3,4, and Martin B. Plenio1

1Institute of Theoretical Physics and IQST, Universität Ulm, Albert-Einstein-Allee 11 D-89081, Ulm, Germany
2QuSoft, Science Park 123, 1098 XG Amsterdam, the Netherlands
3Korteweg–de Vries Institute for Mathematics, University of Amsterdam, Science Park 105-107, 1098 XG Amsterdam, the Netherlands
4Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, the Netherlands

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When two particles interact primarily through gravity and follow the laws of quantum mechanics, the generation of entanglement is considered a hallmark of the quantum nature of the gravitational interaction. However, we demonstrate that entanglement dynamics can also occur in the presence of a weak quantum interaction and non-linear corrections to local quantum mechanics, even if the gravitational interaction is classical or absent at short distances. This highlights the importance of going beyond entanglement detection to conclusively test the quantum character of gravity, and it requires a thorough examination of the strength of other quantum forces and potential non-linear corrections to quantum mechanics in the realm of large masses.

Is gravity fundamentally quantum? One way to answer this question is to try and see whether two particles can get entangled via gravitational interactions. In fact, the entanglement between particles is taken as a hallmark of the quantum nature of gravity. However, this result rests on a hidden assumption: that the theory of quantum mechanics is fundamentally linear, even at the scales where gravity matters. In this work we show how a nonlinear theory with classical gravity (or no gravity at all) could reproduce the same entanglement that one expects from a theory in which gravity is traded as a coherent quantum interaction, opening a loophole in these kind of experiments. We then provide a way to experimentally falsify these nonlinear models, so that the linearity of the theory is certified, and the loophole is closed.

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Cited by

[1] Julen S. Pedernales and Martin B. Plenio, "On the origin of force sensitivity in tests of quantum gravity with delocalised mechanical systems", Contemporary Physics 64 2, 147 (2023).

[2] Ludovico Lami, Julen S. Pedernales, and Martin B. Plenio, "Testing the Quantumness of Gravity without Entanglement", Physical Review X 14 2, 021022 (2024).

[3] Marta Maria Marchese, Martin Plávala, Matthias Kleinmann, and Stefan Nimmrichter, "Newton's laws of motion can generate gravity-mediated entanglement", arXiv:2401.07832, (2024).

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