Two massive bodies frozen in a quantum superposition resemble a pair of dancers trying to keep a single rhythm while an orchestra blares around them. Each gravitational wave is a musician throwing them off beat. In the new work, physicists have shown exactly how this noise destroys quantum coherence — the ability of a particle to exist in multiple states simultaneously.

The problem was that the standard mathematical framework did not allow a clean separation of the system from its environment. The scientists applied a unitary transformation, a kind of coordinate reshuffling, that made the system's momentum depend only on its own observable quantities. It's as if a conductor rearranged the musicians so their sound wouldn't interfere with the dancers hearing each other.

As a result, they obtained the master equation describing the evolution of the quantum system under the influence of gravitational noise. Its dissipative part reproduces the classical energy loss due to gravitational wave emission, while the noise terms suppress coherence between states with different mass quadrupole moments or different proper distances.

In the limit of small quantum fluctuations around the mean distance, the dynamics reduces to a Caldeira–Leggett-type equation with a decoherence rate proportional to the square of the baseline length. This means that the larger the distance between masses, the faster the superposition is destroyed. This dependence is a hallmark of the tidal nature of gravitational waves, and it could help distinguish gravitational decoherence from other noise sources.

Now that the dancers know exactly how the orchestra throws them off beat, they can better prepare for the performance. The derived equation provides quantitative estimates for future experiments with massive quantum systems, such as interferometers. It is a step toward understanding how gravity interacts with the quantum world.