Hawking gave his widely anticpated talk in Dublin today and reports are on CNN and all sorts of other places in the media. Sean Carroll has managed to get ahold (via Dennis Overbye of the New York Times) of a transcript.
Here’s the part where he summarizes his argument:
“I assume the evolution is given by a Euclidean path integral over metrics of all topologies. The integral over topologically trivial metrics, can be done by dividing the time interval into thin slices, and using a linear interpolation to the metric in each slice. The integral over each slice, will be unitary, and so the whole path integral will be unitary.
On the other hand, the path integral over topologically non trivial metrics, will lose information, and will be asymptotically independent of its initial conditions. Thus the total path integral will be unitary, and quantum mechanics is safe.”
His argument is in Euclidean quantum gravity, which he describes as “the only sane way to do quantum gravity non-perturbatively”, something which some might disagree with. What he seems to be arguing is that, while it is true you get information loss in the path integral over metrics on a fixed non-trivial black hole topology, you really need to sum over all topologies. When you do this you get unitary evolution from the trivial (no black hole) topology and the non-trivial topologies give contributions that are independent of the initial state and don’t contribute to the initial-final state amplitude.
I guess what this means is that he is claiming that, sure, if you knew you really had a black hole, then there would be a problem with unitarity, but in quantum gravity you don’t ever really know that you have a black hole, you also have to take into account the amplitude for not actually having one and when you properly do this the unitarity problem goes away.
He has some proposal for doing some kind of calculation that implements his proposal using the AdS/CFT correspondence.