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.
I’m afraid I’ve never followed this whole black hole information paradox story very carefully. It always seemed to me that in the absence of a real theory of quantum gravity, you can’t tell which if any of these proposals really makes sense. People seem to hope that by thinking about this they might make progress on understanding quantum gravity, but I haven’t seen that happen. Spending some time thinking about the Hawking stuff has just reinforced this opinion. He has a vague plausible resolution of the paradox in Euclidean quantum gravity, so do other people in other frameworks. So it looks like the paradox is pretty much gone, which is bad since the hope of many was that solving it would help solve the quantum gravity problem.
By the way, John Baez has a nice first-hand description of the scene in Dublin and a good explanation of Hawking’s argument. See
This week’s finds in Mathematical Physics. Week 207
Peter,
Have you discussed this issue with your Columbia colleague Maulik Parikh? He seems to have another take on the whole debate, the relative simplicity and clarity of which I find appealing. See:
hep-th/0405160
hep-th/0402166
(..not that I know enough to render any kind of a judgment.)
I was there…he didn’t really say that much about anything…i guess we just have to wait for the paper to come out (and even then…ah well, he’s probably right)…Though they havn’t finished up doing the general case (still not done for general geometries and topologies) yet according to his PhD student (i can’t remember his name off hand… ).
It’s hard to tell what really is Hawking’s argument. One sees Maldacena here and a negative cosmological constant there – I don’t know.
Right at the beginning when he says
It sounds as if he is just going to clarify a detail of AdS/CFT.
He does need a negative Lambda to make any sense of the Euclidean path integral, so that’s where the need for AdS comes from. But if he really thinks about going to susystrings on AdS_5 times S5 I don’t know. Before he could come to that he was busy talking about bets and encyclopedias.
I don’t know if one can do AdS/CFT on something else than AdS5 times S5. There are lots of CFT/gravity dualities mentioned in the literature, but I don’t have a good overview. Since it’s really sugra that is involved here, though, every lower dimensional thing must probably come from reducing the full 10d scenario.
The funniest thing is that apparently Witten has done the calculations that are missing in Hawking’s talk already six years ago, as recalled by Jacques Distler.
Well, at various points he is clearly arguing from the point of view of euclidean quantum gravity. I don’t understand how he’s bringing in AdS/CFT other than to show how his ideas are not in conflict with it, at least to the extent you interpret it as a relation between supergravity and a CFT.
By the way, isn’t AdS/CFT about 5d gravity? Can you really use AdS/CFT to study 4d gravity, i.e. is 4d quantum gravity dual to a 3d CFT, and if so which one?
Well, Hawking seems to be relying on AdS/CFT. That tells you the evolution on the gravity side must be unitary. But it also tells you that you don’t have just pure gravity – but susystrings and all that. This again means that it is most likely that the black holes described by AdS/CFT are not just the plain old black holes of Einstein-Hilbert, but have stringy degrees of freedom. It is not clear yet how these should look like. But Mathur has made some educated guesses.
That’s what I found most surprising about Hawking’s talk: He just admitted that old AdS/CFT is the solution to it all and then tried to argue that his Euclidean semiclassical pet is not obviously in conflict with that.
No wonder that this approach raises some eyebrows. Did you see what Susskind commented? 🙂
Decoherence would cause a non-unitary step in the evolution of the system, and a black hole will have to either be formed or not. This is irrespective of the fact that there may be an observer at infinity. The experiment with hot fullerene diffraction shows that a system can cause decoherence with itself if it emits a particle that contains enough information to betray a specific state of the source.
However, the two particles that cause Hawking radiation may be entangled across the event horizon and the state of some particle within the event horizon may be teleported to the particle that escapes away from the horizon.
Somehow the idea seems to be that, asymptotically, the amplitudes for the black hole sector are just constants, don’t depend on the initial state, so I guess they just change the normalization of the overall amplitude.
Important disclaimer: I’m no expert on this stuff, and Hawking’s transcript is so vague that you need a real expert to know what precise sense can be made of his statements. Hopefully he’ll produce a real scientific paper with some details soon.
I read the transcript, and I’m having a basic difficulty. It’s *possible* that a black hole never formed, but the amplitude for that could be incredibly small, no? And yet that amplitude bears the whole burden of storing the information? So when the hole evaporates, you see nothing with probability 1-epsilon, and the information with probability epsilon? That isn’t unitary. Maybe you can tell me if I’m missing something trivial.
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