Existing experiments already provide indirect evidence for the quantum nature of gravity ✛ ✎
Context
The debate over whether gravity needs to be quantized has lasted for decades. The direct route, observing gravitationally mediated entanglement (GME) between two massive particles, requires delocalizing both particles and is currently beyond modern technology. However, in recent years experiments with single delocalized particles have emerged: atoms have been held in superposition over half a meter for more than a minute, and the gravitational Aharonov–Bohm effect was observed in 2022. This work follows that line: it uses a test of the Schrödinger equation for a single system to draw conclusions about the behavior of two systems, relying on the formalism of quantum information and general probability theories.
Methods
The author builds the proof in the language of quantum channels. The unknown time evolution is modeled as a linear map that takes density matrices to density matrices; only positivity (or complete positivity) of this map is required. Two assumptions allow linking the test for one particle to the entanglement of two particles: symmetry of the evolution under particle exchange (analogous to Newton's third law) or dependence of the interaction only on the product of masses (a consequence of the equivalence principle). The analytical proof uses the Choi matrix, while the numerical one uses semidefinite programming with 1000 random states to approximate the positivity condition. Key parameters are taken from realistic proposals: a cesium atom of mass 2·10⁻²⁵ kg, a tungsten sphere of 10 kg at a distance of 3 mm, and an interaction time of 1 s.
Results
Two theorems are proven. The first (qualitative): if the Schrödinger equation holds exactly for a single delocalized particle in the field of a 20 g mass, the evolution is completely positive and symmetric, then gravitationally mediated entanglement is inevitable. The second (quantitative): if the evolution is merely positive and depends only on the product of masses, then it suffices to bound decoherence from above by λ₀ ≈ 0.9995 to guarantee entanglement. Modern interferometers have a phase sensitivity of about 50 μrad, which corresponds to a measurement accuracy of λ₀ better than 1.6·10⁻⁴, and that is enough. Numerical analysis shows that the minimum eigenvalue of the partially transposed density matrix becomes negative at λ₀ ≥ 0.9995, which indicates entanglement.
Implications
The work moves the problem from the experimental to the theoretical plane: there is no need to wait for the construction of complex setups; it is enough to interpret data from existing atomic interferometers. This distinguishes it from neighboring works, which either propose specific GME schemes or discuss whether classical gravity can entangle. Here it is shown for the first time that testing the Schrödinger equation for a single particle, under minimal assumptions, yields a rigorous proof of the existence of GME. The main conclusion is that the bottleneck is not technical but rather the lack of consensus on what observing entanglement means for the quantum nature of gravity.
Future development
The immediate task is to clarify the exact consequences of the existence of GME. It will be necessary to reconcile relativistic locality from quantum field theory with the locality of subsystems from quantum information, possibly within the framework of generalized probabilistic theories. The question of relaxing the assumptions remains open: can one drop symmetry or the dependence on the product of masses? It is also unclear whether requiring only positivity of the evolution is sufficient, or whether complete positivity is justified in the nonrelativistic regime. These questions may be addressed within the program of axiomatizing quantum theory.
Impact
The result will affect the interpretation of experiments in atomic interferometry and discussions about quantum gravity. It also provides a tool for analyzing alternative theories of gravity that do not predict entanglement.
Next steps
Conduct the proposed experiment to test the Schrödinger equation with a single delocalized particle and an external mass to obtain an upper bound on decoherence λ₀. Then apply the numerical method to certify entanglement based on the measured λ₀.
Key open problems
In quantum field theory, the problem of reconciling locality and causality with quantum information remains unsolved. This work directly links the test of the Schrödinger equation to the fundamental question of the nature of gravity, which may stimulate the development of generalized probabilistic theories for quantum fields.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The study uses the Schrödinger equation test for a single delocalized particle in the gravitational field of an external mass, and under two assumptions (symmetry or dependence only on the product of masses) guarantees gravitationally mediated entanglement. Numerical analysis with semidefinite programming yields a quantitative bound of λ₀ ≈ 0.9995, which is achievable with current atomic interferometers.
Where its strength is
It shifts the problem from the experimental to the theoretical plane: it suffices to reinterpret data from existing interferometers, without waiting for complex setups.
Where it could go next
- Nearby is work on gravitational shadows, where mass splits reality; perhaps their formalism could help connect observed decoherence to specific collapse models.based on: Gravitational Shadows: How Mass Splits Reality arXiv:2605.05153v1
- The idea of testing quantumness via rotation from a neighboring work could extend your approach to systems with angular momentum, where the symmetry of evolution manifests differently.based on: Quantum Gravity on a Lab Bench: A Test Through Rotation arXiv:2606.31678
Worth trying
- Check whether the threshold λ₀ ≈ 0.9995 holds for other atomic species, for example rubidium, for which interferometric data are already available.
- Assess the impact of non-gravitational interactions (e.g., van der Waals forces) on the accuracy of the Schrödinger equation test in the proposed scheme.
- Consider using oscillating gravitational fields to enhance the decoherence effect and reduce the required sensitivity.
Why this may matter
If the proposed analysis is accepted, it could accelerate experimental confirmation of the quantum nature of gravity by years, using already existing technologies.
Nearby works in our archive
- Invisible Obstacles in the Hunt for Quantum Gravitysimilarity 0.62
- Gravity Entangles Without Free Fallsimilarity 0.61
- Quantum Gravity on a Lab Bench: A Test Through Rotationsimilarity 0.60
- Gravity Entangles Light and Mattersimilarity 0.59
- Gravitational Shadows: How Mass Splits Realitysimilarity 0.59
- Gravitons Don't Spy on Particlessimilarity 0.58
The closest work in the archive sits at 0.62 by meaning — the usual level for our corpus.
The cesium atom used in the calculations has a mass of 2·10⁻²⁵ kg, which is roughly the mass of 1200 hydrogen atoms. If such an atom were enlarged to the size of a tennis ball, a 10 kg tungsten sphere at the same scale would become the size of the Moon.
Key numbers
- decoherence threshold for entanglement: λ₀ ≈ 0.9995
- sensitivity of modern interferometers: 50 μrad (corresponding to 1.6·10⁻⁴ in λ₀)
- mass of mesoscopic particle for GME: 1.5·10⁻¹² kg
- distance between particles in GME experiment: 5.3 cm
- interaction time: 1 s