Information, Entropy and Black Holes

Last week we talked at length about the observational and astrophysical breakthroughs in black hole physics. The past two decades have also seen a remarkable advancement in the theoretical understanding of black holes. A large part of that science has centered around the black hole information paradox: Black holes are necessarily simple objects about whose contents we can learn nothing. Or can we?

Stephen Hawking famously showed that quantum mechanically, black holes radiate energy. In other words, they glow. Things that glow have a temperature - and from that observation the field of black hole thermodynamics was born.

Because we can’t see inside them - by definition - black holes are parametrized only by a few numbers: like their mass, electric charge and spin. Semiclassical calculations like Stephen’s suggests that the radiation coming out of a black hole should only depend on those numbers as well.

Put differently, information contained in the matter that falls inside a black hole could be lost forever. Since we don’t understand the quantum theory of gravity, Stephen’s analysis was necessarily an approximation. And so a debate has raged for years: do black holes radiate information too?

The connection of information theory to thermodynamics - particularly of the concept of Claude Shannon’s “information entropy” rreinvigorated the debate over the black hole information paradox. Is the information erased? Or is it simply repurposed by quantum mechanics.

Thermodynamically, the surface area of a black hole appears to be directly proportional to its thermodynamic entropy. It appears that black hole physics is more than just gobbling stars and gas. It’s about how those stars and gas are arranged, fundamentally. The more information a black hole sucks in, it would seem, the bigger it gets. Conversely, the more information our universe loses into a black hole, the smaller it gets.

The idea that information loss - erasure - has a thermodynamic cost goes back to Rolf Landauer, and has generated a lot of experimental interest in recent years.

Jonathan O’Callaghan had a great piece in Quanta Magazine this week recounting the history of the Shannon entropy, Landauer ’s eraser and the current experiments investigating its’ predictions. Amusingly, experiments are attempting to construct a physical version of Maxwell’s demon.