What is meant by "information" with regard to general relativity and/or black holes?

Question

In The Universe in a Nutshell chapter 4, Hawking explains the warping of spacetime according to general relativity and introduces the basics of black holes.

It surprised me to read about "information" that fell into the black hole, and then Hawking spends several pages on whether that information is lost. Information? Really? Information, like what team won the Super Bowl, or how tall Danny DeVito is?

I think of information as concepts that have meaning for humans in a cultural context, at a more abstract level than particles, waves, matter, and energy. But clearly Hawking (and others, e.g. Susskind) have a different thing in mind when talking about cosomological information. So what is "information" in this sense? Is it just the physical properties of the particles and waves that fall into the black hole? Even these are human, cultural concepts, aren't they? After all information per se doesn't fall into a black hole, a particle does, and I as an observer might have information on the properties of that particle before it fell, but I don't get in what sense "information" could have fallen into the black hole.

Answer 1

The information in this context is all the variables describing the system. Consider an initial state: a black hole and an electron. This system can be described by position, momentum, mass, charge, angular momentum of the black hole, as well as position, momentum$^\dagger$, mass, charge, spin and kind of particle for the electron.

After the electron crosses the event horizon, the whole system can be described, due to the no-hair theorem, by only a handful of parameters: position, momentum, mass, charge and angular momentum of the black hole. The fact that initially we had an electron, and not e.g. a muon, is lost: we can't "disassemble" the black hole to extract the electron that got into it — even in principle. Kind of particle, and any other information is lost once its "holder" particle has crossed the event horizon.

So, of course, information doesn't fall into a black hole. It's just sloppy language. The particle falls, while information is lost after the particle has fallen.

_{$^\dagger$ I'm ignoring quantum subtleties like Heisenberg uncertainty principle here.}

Answer 2

Consider a vibrating violin string. To predict its motion, it suffices if I know two functions. One function, $y(x)$, specifies its shape, and the other, $v(x)$, gives its initial velocity at each point. If I know the functions $y$ and $v$ at some time $t$, then I can find them at any other time $t'$ using Newton's laws. In this sense, there is information that is never lost.

As a rough analogy for what Hawking is describing, the black hole keeps us from seeing part of the violin string, and the part we can't see gets bigger and bigger.