A recent study has investigated the open quantum dynamics of a system comprising two masses interacting with an environment of linearized gravitational waves. The research focused on the observable proper distance between the two masses. The authors demonstrated that canonical variables derived from the standard Lagrangian formulation, expressed in Fermi normal coordinates, are unsuitable for effectively describing the system. This finding highlights the complexity of modeling the interaction between quantum systems and the gravitational field.

To overcome this limitation, the researchers applied a unitary transformation that enabled a physically meaningful decomposition of the system and its environment. From this new formulation, the master equation of the system was derived, calculated to leading order in the gravitational constant G. The dissipative sector of this equation accurately reproduces the classical energy loss expected due to gravitational wave emission, validating the quantum approximation in the classical limit. Furthermore, the noisy contributions in the master equation suppress coherences between quantum states with different mass quadrupoles, or, effectively, with different proper separations between the masses.

In the regime where the proper distance can be described by small quantum fluctuations around an average distance $l_0$, the system's dynamics simplifies to a Caldeira-Leggett-type equation. This model, widely used to describe decoherence in quantum systems, reveals that the decoherence rate is directly dependent on the baseline length $l_0$. This result suggests that interaction with gravitational waves could be a source of decoherence for quantum systems with significant separations, opening new avenues for understanding quantum-classical boundaries in the presence of gravity.