The gravitational environment cannot be shielded, so it is of particular interest as an unavoidable source of decoherence. Earlier calculations indicated that graviton decoherence of spatial superpositions is noticeable only for systems with momentum on the order of the Planck mass. However, it was recently found that the internal dynamical structure of the system amplifies this mechanism. This work continues that line, adding the influence of the classical Newtonian potential and thereby refining the picture of the quantum-to-classical transition in the presence of gravity.
The authors consider a composite particle with external (center-of-mass position) and internal degrees of freedom, interacting with the quantized gravitational field and the classical Newtonian potential. Using the Feynman-Vernon influence functional formalism, they trace the evolution of the reduced density matrix of the external degrees of freedom. The internal degrees of freedom are modeled as an ohmic environment at high temperature. Gravitons are considered in four initial states: vacuum, thermal, coherent, and squeezed. For simplicity, two configurations of trajectory superposition are analyzed: one with a constant mean position and a changing distance between branches, and another with linearly diverging paths.
In the short-time limit, direct interaction with the graviton bath dominates, and decoherence arises only if the product of mass and velocity significantly exceeds the Planck momentum. For microscopic masses, the effect is negligible. However, in the long-time limit, the contribution from the interaction of gravitons with internal degrees of freedom grows as the cube of time and eventually prevails, making decoherence inevitable even for microscopic masses. For example, for a molecule with a mass of about $10^{-22}$ kg, an internal environment temperature of $10^4$ K, and a superposition size on the order of a nanometer, the decoherence time is approximately $10^5$ seconds (about 1.2 days). The presence of the Newtonian potential slightly slows this process. For systems without internal dynamics, the contribution of the Newtonian potential can lead to formal recoherence, but the corresponding times are comparable to the age of the Universe.
The work shows that the internal structure of a quantum system fundamentally changes the long-time behavior of gravitational decoherence, preventing the saturation characteristic of a point particle. This distinguishes it from neighboring studies that either considered only point particles or did not account for the simultaneous influence of the classical potential. The result is important for understanding the limits of applicability of quantum mechanics and the role of gravity in the measurement process.
Possible generalizations include relativistic particles and quantum fields, as well as other classical backgrounds, such as Schwarzschild or an expanding Universe. An interesting question is whether non-gravitational environments, such as the electromagnetic field, can mediate and enhance gravitational decoherence.
The results may influence the interpretation of experiments with molecular interferometry, levitated nanoparticles, and mechanical resonators, although the observed decoherence times are still too long for modern setups.
The next step could be to study the influence of non-gravitational environments on the enhancement of gravitational decoherence, as well as to consider relativistic corrections and neutrino oscillations.
The work is connected to the fundamental problem of the quantum-classical transition and the role of gravity in wave function collapse. It also touches on the open question of whether the quantum nature of gravity can be experimentally confirmed through indirect decoherence effects.
For relic gravitons, which are assumed to be in a strongly squeezed state with a squeezing parameter on the order of 100, the decoherence time can decrease by a factor of $10^{29}$ compared to the vacuum state.
In Greg Egan's novel Quarantine, quantum superpositions and their collapse under the action of an observer play a central role. The idea that the gravitational environment can irreversibly destroy quantum coherence echoes this plot.