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Why the Black Hole Information Paradox Is Such a Problem
New submitter TheAlexKnapp writes: Here's a really nice explanation of the Black Hole Information Paradox for those who are unfamiliar with it. The article lays out the basic gist — that right now if you take two black holes, one made from the collapse of one type of star, and the second from the collapse of a different type, you can't tell which is which. Ethan Siegel points out that Hawking's big announcement was really just a small step heading towards a possible solution, and highlights that the paradox highlights the incompleteness of our understanding of some types of physics.
In general relativity (our theory of classical gravity, without quantum effects), there are several "no hair" theorems, saying that several types of black holes are completely determined by a few overall parameters (say mass, charge and angular momentum) and without regard to their history.
We don't yet have a theory of quantum gravity, so we don't know if the quantum state of a black hole does retain information. It probably has to, but this is not understood. By the way, in any case classical GR would be an excellent approximation except in the case of very small black holes, so any information retained will not be actually accessible.
No, it is more subtle than that. Conservation of information is closely tied to time reversal symmetry and energy conservation as a result of Noether's theorem. But in general it is not tied to casaulity.
Until then it sounds like: just because you can reverse some signs and run your equations backwards doesn't mean that all math has a physical reality.
Nope, Noether's theorem is quite specific, and if there are certain symmetries in your equations (i.e. you can just reverse some signs for on example), then there exists certain conservation laws. If there is time symmetry in the equations, then it is a necessary consequence of the equations that energy is conserved. This has nothing to do with reality of math or if time can actually be reversed... either the particular equations are correct or not. If they are correct, then all logical consequences of the equations are also correct.