A black hole horizon is like a soap film stretched over an abyss. From a distance it looks perfectly smooth, but up close it trembles. This ripple arises from quantum fluctuations — the continuous birth and death of particles in the vacuum.
Physicists studied such trembling for a black hole in three-dimensional space with negative curvature (as in a universe with anti-de Sitter geometry). They gave a clear recipe for measuring the amplitude of the oscillations and called it the "quantum width" of the horizon. Using the holographic principle, the idea that gravity inside a volume is fully described by a theory on its boundary, they linked the width to familiar quantities at the edge.
It turned out that the typical amplitude of the trembling is roughly the fourth root of the product of the gravitational constant and the cube of the space radius. In numbers, this is far larger than the Planck length (the smallest possible size). Moreover, the smaller the scale you look at, the stronger the horizon trembles — in the limit of zero size, the fluctuations diverge logarithmically.
This result is the most reliable evidence to date that quantum fluctuations of the horizon are real and noticeable without any tricks. The trembling of the film is not just a theoretical curiosity but a direct consequence of quantum gravity as currently understood.
You can picture the quantum width of the horizon as the trembling of a soap bubble shaken by the thermal motion of air molecules — except here the "molecules" are virtual particles of the vacuum.
In the book "Black Holes and Time Warps," Kip Thorne describes quantum foam on the horizon: it is precisely these properties that this work refines.