Friday, April 07, 2006

Two preprints on information loss

I kind of agree with many of the statements but have not quite understood what we learn from these comments. This situation can of course change if someone explains me the point.

Vijay, Donald, and Moshe argue that - if you allow me to use a particular example and try to say what they say in a more transparent way - the spectrum of operators in N=4 gauge theory is discrete. This also means that the spectrum of the Hamiltonian of the gauge theory on "S^3 x R" is discrete, too, which implies that the spectrum of the Hamiltonian in the global "AdS5 x S5" is discrete, and if you measure it with the exponential accuracy, you can distinguish the microstates from each other. It's still true if the dimension of the operators is much larger than one - and generic states of this type describe microstates of the stable (large) AdS black holes. Because you can measure the microstate at infinity, the authors argue, no information is lost.

The main reason why I think that this does not really answer any of the deep questions about the information loss is that for stable black holes, we could have always believe that the information was preserved. If something is exactly static, then everything about it - including the information - is preserved. You can always believe that the information is stored inside the black hole. You don't see inside the black hole but you can't prove that it's lost. The information loss paradox only becomes sharp when you consider a black hole that evaporates and when you argue that the radiation is a mixed thermal state. But for evaporating black holes, their arguments completely break down. The evaporating black holes are not eigenstates but metastable states with a lifetime comparable to the evaporation lifetime: the corresponding width (an error of the measurements of energy) is a power law of the energy which is exponentially greater than the resolution of energy you need to identify the microstates. So I don't think that we learn much except for the old well-known fact that the unitarity of everything in gauge theory is manifest.

Steve Giddings had a paper about the same topic of information loss and he argued for a pretty drastic violation of the semiclassical picture. But because the paper was later withdrawn, I won't comment on it.

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