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Information Paradox *January 16, 2009*

*Posted by keithkchan in Quantum Gravity.*

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Recently, information paradox is rather popular in the blogosphere, at least in the blogs I read. First Moshe gave a post on the Maldacena’s information paradox, and Lubos Motl gave a follow-up post on Killing the information softly, explaining why information is lost in irreversible process. I asked Lubos Motl some questions, and I feel enlightened from his reply, so I would like summarize what I learn here. Of course I have no expertise or whatsoever in this problem, any faults in the interpretation is mine and you should consult the original posts if you are interested in.

First let me summarize the information paradox. Suppose there is a black hole. You throw something, say a book, into it. It got sucked into the black hole, and the info in the book can never be retrieved. Black hole does churn out the Hawking radiation, but it is of the blackbody spectrum, with least information, so you can’t reconstruct the book from the radiation. This problem in the intersection between general relativity (GR) and quantum mechanics (QM). If you believe in GR, then info is truely lost, while the fundamental unitarity requirement in QM demands that info to be preserved. Of course this problem stems from the fact that there is no consistent theory of quantum gravity.

What Maldacena shown was that in the anti de Sitter space, the gravity theory can be mapped to a gauge field theory by the AdS/CFT correspondence, in which the information is shown to be preserved. When the theory is truncated and GR approximation is taken into account, info is apparently lost. According to Lubos, this implicitly requires string theory since it is the only fully consistent quantum theory of gravity. So it seems that QM prevails. For some people this info paradox is not yet settled since it has only been shown in AdS space, while our universe is not AdS. Why work in AdS space? I quote Lubos’ reply to my question here

The anti de Sitter space has many technical advantages. For example, the signals reflect from the boundary at infinity after a finite time of an observer inside, so the space is effectively compact (it is similar to compact spaces when it comes to causality) even though the proper volume is infinite. Also, its volume effectively scales like the surface, which makes holography partly automatic.

Most importantly, there exists an equivalent description of the AdS space in terms of a theory on the boundary at infinity, the so-called “holographic” AdS/CFT correspondence by Maldacena. Whenever this equivalence is firmly established, it is in contexts where strings exist – a kind of string theory. But you might also say that the AdS/CFT map is more general, except that no other fully consistent theories of quantum gravity truly different from string theory are known. Sociologically speaking, there are people who use AdS/CFT and don’t fully accept string theory as the only possible consistent theory of quantum gravity, but they’re just not studying these issues quite accurately.

I believe that GR is not the ultimate theory and info is preserved.

PS. You may notice that I have added Lubos Motl to the blogroll. His explanation in physics is superb, that is for sure, but some of his opinions I disagree such as his anti-climate change view point. You may want to filter out those nonsense, and pick up the gems.

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