Gravity That Pushes Away: Quantum Superposition Against Attraction
Context
Gravity remains the last of the fundamental forces without a generally accepted quantum theory. Experiments with neutrons and atoms in a gravitational field show only that quantum particles feel classical gravity, but they do not prove that the field itself is quantum. A whole research direction has already grown around this work: some groups propose looking for entanglement created by gravity, others test how gravity behaves under measurement. This paper sits in the same current, but offers a qualitatively different test: instead of entanglement, it uses an anomalous weak value that flips the sign of the force.
Methods
The scheme involves two massive objects: a source (mass 1) and a test particle (mass 2). The source passes through a Stern-Gerlach interferometer, where its spin controls its position in space, creating a superposition of two trajectories. The test particle starts in the ground state of a harmonic trap, then is released and moves freely under the gravity of the source. After interferometry, the source undergoes postselection: a spin state is measured that corresponds to an anomalously large and negative weak value of the projection onto the trajectory closer to the test particle. This causes the momentum transferred to the test particle to change sign and to be amplified by a factor of 1/ε, where ε is the small asymmetry parameter of the initial superposition.
Results
With postselection probability ε²/4 ≈ 2.5×10⁻⁵, the test mass receives momentum directed away from the source, that is, an effective gravitational repulsion is observed. For realistic parameters (masses ~10⁻¹⁴ and 10⁻¹² kg, distance 20 μm, interferometry time 1 s, momentum squeezing η~0.35), the expected displacement of the test particle over 10 s is about 1 Å, which is already accessible to measurement. The total probability of successfully detecting a repulsion event is estimated at 2.5×10⁻⁷, so on the order of 4×10⁷ repetitions of the experiment would be required.
Implications
Unlike neighboring works, where the quantumness of gravity is proven through entanglement, here a weak measurement with postselection is used. This is a fundamentally different method: it does not require creating an entangled state between the masses, but relies on interference of amplitudes in the source itself. If the experiment succeeds, it would be direct evidence that the gravitational field can be in a superposition of states, and therefore that spacetime obeys the laws of quantum mechanics.
Future development
The proposed scheme can be extended to larger masses and larger superpositions. Improvements in cooling and momentum squeezing techniques will reduce the required number of repetitions. The method could be adapted to test other quantum effects of gravity, for example, quantum fluctuations of the metric. It would also be interesting to study how repulsion depends on distance and mass, in order to compare with the predictions of specific theories of quantum gravity.
Impact
The result will affect fundamental physics: quantum field theory in curved spacetime, theories of quantum gravity, and interpretations of quantum mechanics. In practical terms, it will stimulate the development of nanoparticle levitation technologies, precision measurements of weak forces, and quantum control of macroscopic objects.
Next steps
The nearest step is to implement Stern-Gerlach interferometry for a nanocrystal with a mass of 10⁻¹⁴ kg and a coherence time of about 1 s. Then it will be necessary to integrate a trap for the test mass and a system for precisely measuring its position with subangstrom resolution.
Key open problems
The work is directly connected to the problem of the quantum nature of gravity, one of the main open questions in theoretical physics. It also touches on the problem of the quantum-classical transition: up to what scales does quantum superposition survive, and how does it manifest in gravitational interaction. The success of the experiment would help choose between purely quantum and semiclassical models of gravity.
The weak value of the projection can be negative and greater than one in magnitude, which looks as if the particle is in a place where there is 'less than nothing' of it. It is precisely this paradoxical effect that turns attraction into repulsion.
The idea of gravitational repulsion vaguely resembles the 'gravitsapa' from the film Kin-dza-dza!, but there it is pure fantasy, whereas here it is a strict consequence of quantum mechanics.
Key numbers
- postselection probability: 2.5×10⁻⁵
- expected displacement of the test mass: 1 Å over 10 s
- required number of repetitions: 4×10⁷
- source mass: 10⁻¹⁴ kg
- distance between masses: 20 μm