Gravity as Noise: Why Macroscopic Objects Lose Quantum Coherence ✎
Context
Quantum superpositions of massive objects underpin matter-wave interferometry, levitated particles, and optomechanical systems. These platforms push quantum control toward larger masses and lengths, and are used for quantum-enhanced sensing and tests of the quantum nature of gravity. The key question is how quickly coherence is lost through interaction with the environment. Typically, electromagnetic noise, thermal radiation, and collisions with residual gas dominate. Gravity, however, is long-range, universal, and unscreenable, so even a rarefied gas can create an additional decoherence channel. The standard collisional model is inapplicable here because of infrared divergences. This work sits alongside research on gravitational decoherence and quantum gravity, but stands out for its first-principles derivation and its inclusion of finite size and observation time.
Methods
The authors use the closed-time-path formalism (influence functional) for open quantum systems. The starting model: linear gravity, a massive point particle, and a scalar environment field. The metric is expanded around Minkowski space, and the de Donder gauge is imposed. After integrating out the gravitational and scalar degrees of freedom, an influence functional is obtained that depends on the difference of energy-momentum tensors on the two branches of the contour. To regularize singularities, window functions in time and space are introduced, along with a Gaussian profile for the finite system size. For the rarefied gas, a wave-packet model with a Maxwellian velocity distribution is used. In the nonrelativistic limit, decoherence reduces to a one-dimensional integral over momenta.
Results
An analytical formula for decoherence is obtained: Γ ∝ M² Δx² ln(k_UV/k_σ), where M is the system mass, Δx is the separation between superposition branches, k_UV is the ultraviolet scale (inverse system size), and k_σ is the infrared scale (inverse wavelength of thermal fluctuations). The logarithmic contribution accumulates over a wide range of distances from k_UV^{-1} to k_σ^{-1}. For typical parameters (M = 10^{-17} kg, Δx = 10^{-8} m, nitrogen at atmospheric pressure), Γ ≈ 10^{-26} per second. This is many orders of magnitude smaller than collisional decoherence (the ratio Γ/Γ_col < 10^{-20} in most regimes). Even for aggressive quantum-gravity parameters (M ~ 10^{-14} kg, Δx ~ 250 µm), Γ ~ 10^{-13}, which is still negligible.
Implications
The work provides a rigorous first-principles derivation of gravitational decoherence from fluctuations of environmental matter. Unlike previous approaches that often used phenomenological models or ignored finite size, here window functions and a source profile are explicitly introduced. This allows quantitative assessment of the contribution for real experiments. The result confirms that gravitational noise from gas is not an obstacle for quantum technologies, but sets an upper bound on effects that could be detected in future experiments testing the quantum nature of gravity.
Future development
The formalism can be extended to more general media, including photons, neutrinos, or dark matter. Accounting for the quadrupole moment instead of the dipole approximation will refine the infrared behavior. It may be possible to include nonlinear gravitational effects and self-gravity. For experiments with levitated particles in high vacuum, accounting for gravitational noise from vacuum fluctuations of the gravitational field itself may become relevant.
Impact
The results are important for matter-wave interferometry, levitated nanoparticles, and optomechanical systems, where decoherence limits coherence time. They also set a benchmark for experiments testing the quantum nature of gravity through entanglement of massive bodies.
Next steps
Generalize the model to quadrupole order and account for compensation of the dipole moment by the surrounding apparatus. Investigate decoherence from gravitational waves and quantum fluctuations of the metric. Perform numerical simulations for specific experimental setups.
Key open problems
In quantum gravity, it remains an open question whether gravity causes decoherence by itself, without the mediation of matter. This work shows that the contribution from material fluctuations is negligible, which heightens interest in searching for intrinsic gravitational effects. There is also the ongoing problem of reconciling quantum mechanics and general relativity on macroscopic scales.
The logarithmic dependence of decoherence on the ratio of ultraviolet to infrared scales resembles the behavior of infrared divergences in quantum electrodynamics, where logarithms of mass ratios also arise.
In The Expanse, quantum computers aboard ships require isolation from gravitational disturbances, which echoes the idea of gravitational noise as a source of decoherence.
Key numbers
- Decoherence for M=10^-17 kg, Δx=10^-8 m: 1.2×10-26 per second
- Typical mass of a levitated particle: 10-17 kg
- Separation between superposition branches: 10-8 m
- Gas density (nitrogen at 1 atm): 2.4×1025 m^-3
- Typical thermal speed of nitrogen molecules: 480 m/s