### To loose or not to loose information

#### Posted by Urs Schreiber

Over here and here a link to a transcript of Stephen Hawking’s talk on the *apparent black hole information loss problem* can be found.

The key argument in, well, a nutshell, is that the Euclidean path integral for gravity over topologically trivial manifolds gives an invertible mapping from initial to final configuration, while that over topologically non-trivial manifolds does not.

Hawking concludes from that that the *total* path integral will be unitary.

I am looking forward for seeing this detailed in a paper, because I am not sure what to make of it. Something unitary plus something non-unitary certainly does not give us something unitary, so this cannot be what is meant. I would understand the final claim if we had *restricted* ourselfs to the path integral over trivial topologies, but is this what is meant?

[**Almost immediate update**: Ah, now I get it, the idea is that the contribution from the nontrivial topologies completely factors to a constant and can be devided out. ]

In the talk, the AdS/CFT correspondence is mentioned frequently. Right at the beginning it seems like Hawking is crediting AdS/CFT and hence Maldacena for giving the solution to the information paradox and that his talk is merely supposed to elucidate how this happens in detail on the gravity side of the duality.

What I find puzzling is that AdS/CFT makes the ‘gravitational’ path integral well defined by giving it a UV-completion, namely string theory. Hawking on the other hand argues purely from the Euclidea path integral for Einstein-Hilbert gravity as well as its canonical quantization. But as far as I know the Euclidean path integral is only gradually better behaved than the Lorentzian one, Wick rotation in a scenario where no background metric and much less timelike isometries are present is a mystery, really, and finally nobody knows how and even if that canonical Hamiltonian operator of pure gravity can be defined, which Stephen Hawking argues to generate the unitary time evolution.

Some work by Maldacena on 3-dimensional AdS gravity is mentioned which seems to support the main claim that information loss and non-unitarity is related to nontrivial topologies, but I don’t know about the details here.

The last but one part of the talk is concerned with a rough (looks hand-waving, indeed, but it is not clear to me which omissions are due to the nature of the talk or actually due to unsolved problems) argument how one could go about actually calculating a solution which shows the unitary formation and evaporation of something that would be a black hole for practical purposes.

The very last part of the talk is about merchandising in theoretical physics. :-)

Posted at July 22, 2004 11:21 AM UTC
## Re: To loose or not to loose information

Ok, theres a few things that bother me technically, maybe someone can help me here.

One… Why is the Euclidean path integral being used in a semiclassical regime, and only to 2 orders it seems. Usually, its the late orders of perturbation series that reveal the semiclassical limit of the theory (take the anharmonic oscillator as an example)

Two.. I don’t follow the argument that the nontrivial topologies factor to a constant, or alternately that the nonunitarity goes away asymptotically. Why exactly? He mentions that there is no conserved quantities (which strikes me as more a problem with the way time is defined here, eg a mathematical problem, not necessarily a physical one)

I don’t have a problem with taking the values at the boundary, but I don’t get the relevance of ADS/CFT either in this situation.