Light falling into a black hole carries information — for instance, the path a photon took. The horizon (the surface from which nothing returns) responds by changing its entropy — a measure of disorder, akin to the number of shuffled pages in a book. But light is made of quanta, and the quantum world abhors total silence: there is always a tremor — random fluctuations, like ripples on water stirred by wind.
In a new study, physicists show that this tremor fundamentally limits information recording. They considered a thought experiment where photons encode information about the path they traveled and derived an ironclad rule. It turns out that the spread (statistical variance) of the black hole's entropy change and the number of photons are inversely related. Want to record information more precisely? Send more photons, but then the entropy itself trembles more. Want to reduce the tremor? You sacrifice the number of particles.
This result is obtained within stochastic semiclassical gravity — an approach where spacetime is described by Einstein's equations, but with an added noise from quantum fields. Such noise is inevitable, like static in an old radio. The authors emphasize: the horizon cannot record quantum information with arbitrarily small entropy fluctuations. There is always an irreducible tremor, like a scale that sways with every breath, preventing a perfectly precise weighing.
The horizon area of a black hole with the mass of the Sun is about 12 square kilometers, and its entropy is 10²⁰ times greater than that of the Sun, which is composed of hydrogen and helium.