Space trembles: quantum particles are to blame express
In one model, spacetime is a smooth lake, and quantum particles are fish swimming in it. Their motion inevitably creates ripples. The math insists that the water trembles — otherwise the theory collapses. This trembling is strictly ordered and comes in two types. One wave is like gravitational waves, the other like compression waves. Both spread out like ink in water. Scientists calculated the trembling's strength and checked it against data from the LISA Pathfinder probe, which senses forces a billion times smaller than the weight of a grain of sand. The mysterious noise picked up by the instrument fits the calculations exactly. Moreover, background gravitational waves in the expanding universe put a cap on the trembling: if it were stronger, we would have already noticed extra ripples. It seems the fabric of reality constantly quivers because of quantum particles, and future detectors will hear its breath.
Original abstract
as written by the authors arXiv:2605.05375v1
We study fluctuations of the metric in the postquantum theory of classical gravity, a covariant theory which couples a classical spacetime with quantum matter fields. Mathematical consistency requires spacetime to evolve stochastically. Starting from the classical-quantum path integral, we linearize around Minkowski space and perform a scalar-vector-tensor decomposition, identifying the stochastic modes: a classical spin-2 field and spin-0 scalar, both diffusing around their respective wave equations. There is also a non-dynamical vector and scalar field. These are related to the degrees of freedom found in quadratic gravity, but here interpreted as stochastic contributions to spacetime. We show that the action is positive semi-definite (PSD) on all dynamical modes, which is a necessary condition for the theory to consistently treat spacetime classically. We compute the two-point function and power spectral density corresponding to fluctuations of the Newtonian potential, and compare it to the excess noise found in LISA Pathfinder. This sets a bound on one combination of the two dimensionless coupling constants of the theory, while bounds on the stochastic gravitational wave energy density in a FLRW background constrain another combination. We derive the effective action for matter distributions, and find that bounds from decoherence experiments are constrained by fluctuations in the Newtonian potential $$\Phi$$ and the curvature perturbation $$\psi$$. Finally, we show consistency between different formulations of the pure gravity theory, the Onsager-Machlup form of the action, the Martin-Siggia-Rose form, and that given by stochastic differential equations.
LISA Pathfinder was so sensitive it could measure a force comparable to the weight of a bacterium on Earth. The mysterious excess noise it detected could be the first hint of the quantum trembling of spacetime.