Drop a pebble into a pond, and ripples spread across the water. In much the same way, any body, even the tiniest, perturbs the gravitational field around it. In empty, cold space, these perturbations, like ripples on a calm surface, make two nearby objects always repel each other. This phenomenon is called the Casimir–Polder gravitational interaction. But what happens if the pond is not calm but heated, full of thermal ripples?
The authors added a "thermal wind" of gravitons, the tiny carriers of gravity, to the picture. In a hot environment, they dart about chaotically, like steam molecules above boiling water. The scientists considered a simple scene: a tiny object hangs near a perfect wall that blocks gravitational waves. Under gravity's influence, the object can polarize — slightly stretch out, like iron filings in a magnetic field. In the cold, when thermal gravitons are almost absent, the force depends only on distance and always pushes the object away from the wall. Turn on the heat, and the picture becomes richer.
The most unexpected finding emerged at high temperatures. If the object polarizes along the wall, the force falls off very slowly with distance — following the law $T/L$, where $T$ is temperature and $L$ is distance. If it polarizes perpendicular to the wall, the force suddenly becomes attractive. And when the thermal ripples get really turbulent, the force starts to oscillate: at some distances the wall pulls the object toward it, at others it pushes it away. All this means thermal gravitons are not just noise. They are an active tool that can be used to control quantum gravitational forces.
The Casimir–Polder gravitational interaction is an analog of the famous Casimir effect from electrodynamics, but for gravity. In the ordinary Casimir effect, two plates in a vacuum attract each other due to quantum fluctuations; here, a single object interacts with a boundary, and in vacuum the force is always repulsive.
In the novel 'The Doomed City' by the Strugatsky brothers, the characters encounter a mysterious wall that changes its properties depending on external conditions — somewhat similar to how thermal gravitons change the nature of an object's interaction with a gravitational boundary.