Gravity as Noise: Why Macroscopic Objects Lose Quantum Coherence ✎

On a laboratory table, a tiny particle levitates, held by a laser beam. It is in a quantum superposition: its wave function describes two positions simultaneously, as if the particle had split in two. But this state is not eternal. The surrounding world constantly interferes, and quantum coherence fades like morning mist. Usually, collisions with gas molecules and electromagnetic noise are considered the main culprits. However, there is a subtler channel: gravity.

Gravity is a quiet whisper that gets lost in the loud noise of collisions. Each gas molecule attracts the particle, and if the particle is in a superposition of two positions, the gravitational field acts differently on each position. This difference destroys quantum interference. The problem is that gravity is long-range and unscreenable: even a very rarefied gas can contribute. Scientists from Kyoto University have constructed a first-principles theory of this process. They used the closed-time-path formalism to accurately account for quantum fluctuations of the gravitational field generated by the gas. For a rarefied nonrelativistic gas, they managed to obtain an analytical formula:

\[ \Gamma \propto M^2 \Delta x^2 \ln(k_{UV}/k_\sigma) \]

Here \(M\) is the particle mass, \(\Delta x\) is the distance between the two branches of the superposition, and \(k_{UV}\) and \(k_\sigma\) are the ultraviolet and infrared scales. The logarithmic dependence means that decoherence accumulates slowly but covers a huge range of distances, from the size of the particle itself to the wavelength of thermal fluctuations of the gas. This resembles the behavior of infrared divergences in quantum electrodynamics, where logarithms of mass ratios also arise.

The result may seem disappointing: gravitational noise from the gas is not an obstacle for quantum technologies. But that is precisely the value of the work. Previously, it was unclear whether long-range gravity could cause noticeable decoherence through interaction with a rarefied gas, and how to correctly account for infrared effects. Now we know that the contribution exists, but it is negligibly small. This provides a quantitative benchmark for future experiments testing the quantum nature of gravity. If one day it becomes possible to create a superposition of a sufficiently massive object, gravitational noise from the environment will not prevent observing subtler effects associated with quantum fluctuations of the gravitational field itself.

The formalism developed by the authors can be extended to other media: photons, neutrinos, dark matter. Taking into account the quadrupole moment instead of the dipole approximation will refine the infrared behavior. Perhaps in the future we will learn to measure gravitational noise from vacuum fluctuations of the metric. Then the quiet whisper of gravity will cease to be merely a theoretical abstraction and become an observable phenomenon.