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Proposed experiment shows that quantum entanglement is not the only way to test whether gravity has a quantum nature

1 May 2024

Successfully combining quantum mechanics and gravitational physics is one of the main challenges of modern science. Generally speaking, progress in this area is hindered by the fact that we cannot yet perform experiments in regimes where both quantum and gravitational effects are relevant. At a more fundamental level, as Nobel Prize laureate Roger Penrose once put it, we do not even know whether a combined theory of gravity and quantum mechanics will require a ‘quantisation of gravity’ or a ‘gravitisation of quantum mechanics’. In other words: is gravity fundamentally a quantum force, its properties being determined at the smallest possible scales, or is it a ‘classical’ force for which a large-scale geometrical description suffices? Or is it something different yet?

It has always seemed that to answer these questions, a central role would be played by the typically quantum phenomenon of *entanglement*. As Ludovico Lami, mathematical physicist at the University of Amsterdam and QuSoft, puts it: “The central question, initially posed by Richard Feynman in 1957, is to understand whether the gravitational field of a massive object can enter a so-called *quantum superposition*, where it would be in several states at the same time. Prior to our work, the main idea to decide this question experimentally was to look for gravitationally induced entanglement – a way in which distant but related masses could share quantum information. The existence of such entanglement would falsify the hypothesis that the gravitational field is purely local and classical.”

The main problem with the previous proposals is that distant but related massive objects – known as delocalised states – are very challenging to create. The heaviest object for which quantum delocalisation has been observed to date is a large molecule, much lighter than the smallest source mass whose gravitational field has been detected, which is just below 100 mg – more than a billion billion times heavier. This pushed any hope of an experimental realisation decades away.

In the new work, Lami and his colleagues from Amsterdam and Ulm – interestingly, the place where Einstein was born – present a possible way out of this deadlock. They propose an experiment that would reveal the quantumness of gravity without generating any entanglement. Lami: “We design and investigate a class of experiments involving a system of massive ‘harmonic oscillators’ – for example, torsion pendula, essentially like the one that Cavendish used in his famous 1797 experiment to measure the strength of the gravitational force. We establish mathematically rigorous bounds on certain experimental signals for quantumness that a local classical gravity should not be able to overcome. We have carefully analysed the experimental requirements needed to implement our proposal in an actual experiments, and find that even though some degree of technological progress is still needed, such experiments could really be within reach soon.”

Surprisingly, to analyse the experiment, the researchers still need the mathematical machinery of entanglement theory in quantum information science. How is that possible? Lami: “The reason is that, although entanglement is not physically there, it is still there in spirit — in a precise mathematical sense. It is enough that entanglement *could have been* generated.”

The paper in which Lami and colleagues explain their findings was published in Physical Review X this week. The researchers hope that their paper is only the beginning, and that their proposal will help design experiments that may answer the fundamental question about the quantumness of gravity much earlier than expected.

*Testing the quantum nature of gravity without entanglement*, Ludovico Lami, Julen S. Pedernales and Martin B. Plenio, Physical Review X, 2024.

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