Gravitational decoherence is the decay of quantum superpositions of an object due to interaction with gravitational degrees of freedom, such as gravitational waves. This phenomenon attracts attention as a potential tool for understanding the interplay between gravity and quantum theory. Decoherence depends on the form of the interaction Hamiltonian, so the details of the effective system dynamics can shed light on how gravity couples to quantum matter. In light of possible experimental tests, the weak-field regime where gravity is linearized is sufficient for practical purposes. However, deriving a suitable Hamiltonian for open quantum system dynamics is nontrivial due to the need for an unambiguous separation of system and environment.
The authors consider a system of two masses in a weak gravitational field described by the Minkowski metric with a small perturbation. Fermi coordinates are used, in which the proper distance between the masses is given by the geodesic deviation vector. The interaction Lagrangian contains second derivatives of the metric perturbation, complicating standard quantization. To circumvent this, the authors first integrate by parts to obtain a Lagrangian with first derivatives, then apply a unitary transformation that redefines the canonical variables so that the system momentum depends only on its proper observables. Subsequently, they derive the master equation for the reduced density matrix using the Feynman–Vernon influence functional formalism, assuming an initially factorized state and a thermal state for the gravitational environment.
A master equation is obtained for a system of two masses interacting with linearized gravitational waves, to leading order in G. The dissipative part reproduces the classical formula for energy loss via gravitational wave emission: ⟨d⟨E⟩/dt⟩ = −(16/15) G I² ω⁶ / c⁵, where I is the mass quadrupole moment. The noise terms cause decoherence of superpositions of states with different proper distances. In the limit of small quantum fluctuations around the mean distance l₀, the dynamics reduces to a Caldeira–Leggett-type equation with a decoherence rate Γ ∝ l₀². This rate is proportional to the square of the difference in potential energies in the superposition divided by the Planck energy, and to the temperature of the gravitational background.
This work resolves a long-standing problem of correctly describing open quantum dynamics in the presence of gravity. It shows that the choice of canonical variables is critical for obtaining a physically meaningful master equation. The derived equation can serve as a basis for quantitative predictions of gravitational decoherence in future experiments, e.g., with interferometers. The dependence of the decoherence rate on the baseline length l₀ is a characteristic feature of the tidal nature of gravitational waves and may help distinguish gravitational decoherence from other noise sources.
Future work could investigate non-Markovian corrections and consider non-Gaussian states of the gravitational environment, such as squeezed states that may arise in cosmology. It is also of interest to study decoherence for more realistic configurations, including all polarizations and propagation directions of gravitational waves, which is partially done in the appendix. The approach might be extended to other systems, e.g., spin degrees of freedom.
The results could influence the interpretation of experiments testing quantum gravity and the development of gravitational wave detectors sensitive to quantum effects. They also refine theoretical models of decoherence in cosmology and black hole physics.
The next step could be deriving the master equation for more general states of the gravitational background and including higher orders in G. It is also important to connect predictions with specific experimental setups, such as interferometers with large masses.
In open quantum systems physics, the question of how gravity affects quantum coherence of macroscopic objects remains open. This work contributes to solving the problem of correctly defining system observables when interacting with a gravitational field and provides quantitative estimates of the decoherence rate, directly related to the fundamental problem of the quantum-to-classical transition.
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What the work does
The work derives the master equation for a system of two masses interacting with linearized gravitational waves, using Fermi coordinates and a unitary transformation to correctly separate the system from its environment. The resulting dissipation reproduces the classical energy loss to gravitational radiation, while the noise contributions cause decoherence of superpositions with different proper distances. In the limit of small fluctuations, the dynamics reduces to a Caldeira–Leggett-type equation with a decoherence rate proportional to the square of the baseline length.
Where its strength is
The key contribution is the careful construction of a physically meaningful interaction Hamiltonian via a unitary transformation that removes the ambiguity in the canonical variables. This provides a solid foundation for quantitative predictions of the decoherence rate and its connection to classical radiation, which can be built upon when extending the model.
Where it could go next
Worth trying
Nearby works in our archive
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The decoherence rate is proportional to the square of the distance between the masses. This means that increasing the baseline length of an interferometer not only enhances sensitivity to gravitational waves but also accelerates the loss of quantum coherence, a sort of price for size.
The idea that gravitational waves could destroy quantum superpositions echoes the concept of 'quantum foam' in Greg Egan's novel 'Schild's Ladder', where spacetime fluctuations affect quantum processes.