July 22, 2004

No Information Lost Here!

The blogosphere — or, at least, that little corner of it that I pay attention to — is all a-twitter about Hawking’s announcement that he has solved the blackhole information problem (30 years after posing it). Normally, I try not to devote attention to such things, but the flurry of discussion prompted me to take a look at the transcript of Hawking’s talk.

He starts off with the amusing comment,

I adopt the Euclidean approach, the only sane way to do quantum gravity non-perturbative [sic].

Of course, among its other defects, the Euclidean path-integral he wishes to do is horribly infrared divergent. So his first step is to introduce an infrared regulator, in the form of a small negative cosmological constant. This is not merely a technicality. None of the subsequent arguments make any sense without it.

Anyone who hasn’t been asleep for the past 6 years knows that quantum gravity in asymptotically anti-de Sitter space has unitary time evolution. Blackholes may form and evaporate in interior, but the overall evolution is unitary and is holographically dual to the evolution in a gauge theory on the boundary.

With the large accumulation of evidence for AdS/CFT, I doubt there are many hold-outs left who doubt that the above statement holds, not just in the semiclassical limit that Hawking considers, but in the full nonperturbative theory.

Nonetheless, a “bulk” explanation of what is going on is desirable, and Hawking claims to provide one. Hawking devotes a long discussion to the point that trivial topology dominates the Euclidean path-integral (at zero temperature). Since the trivial topology can be foliated by spacelike surfaces, one can straightforwardly Wick-rotate and it follows that Minkowski-signature time evolution is unitary. Presumably, Hawking is aware of, but neglected to mention Witten’s old paper, which not only show the dominance of the trivial topology at low temperature, but shows that, at high temperature, the path integral is dominated by the Hawking-Page instanton (the analytic continuation of the AdS blackhole) and that, moreover, the phase transition which separates these two regimes (which Hawking and Page argued for, in the context of semiclassical gravity in AdS) is related to the confinement/deconfinement transition in the large-N gauge theory.

All of these are true facts, well-known to anyone familiar with AdS/CFT. But the latter goes well beyond the semiclassical approximation that Hawking uses. No one (at least, no one I talk to) has the slightest doubt that quantum gravity has unitary time evolution in asymptotically AdS space. The blackhole information paradox is solved in AdS, and it was “solved” long ago.

However, most people agree that the extrapolation to zero cosmological constant is not straightforward. There still room to doubt that time evolution in asymptotically flat space is unitary. On the thorny issue of extrapolating to zero cosmological constant, Hawking is silent.

Posted by distler at July 22, 2004 11:35 AM

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Excerpt: Stephen Hawking gave his talk yesterday, the media came and went, and now the interpretations are beginning to trickle onto the web. The...
Tracked: July 22, 2004 5:07 PM

Re: No Information Lost Here!

I’m sure these comments are on the money (Hawkings, not Thornes ;-) but the last paragraph got me thoroughly confused.

Since one of the ways to approach flat space asymptotically should be by decreasing a small negative cosmological constant in a close facsimile to flat space in the nonzero constant space, it should follow from your/Hawking arguments that a useful simile to flat space is unitary?!

Does one really need true flat space, and if it isn’t unitary, does it exist (in QG)? Or is that the question?

Posted by: Torbjörn L on July 23, 2004 11:36 AM | Permalink | Reply to this

Almost flat

The problem is that what we really would like to have is some analog of AdS/CFT but for a small but positive cosmological constant, because that’s what we currently seem to observe.

Posted by: Urs Schreiber on July 23, 2004 1:38 PM | Permalink | PGP Sig | Reply to this

Taking Λ to zero

The nature of the observables in AdS space (the correlation functions of a field theory on the conformal boundary) and the observables in flat space (an S-matrix) are very different.

Presumably, there is a map between the $\Lambda \to 0$ limit of the former and the latter. But constructing that map is highly nontrivial.

Urs would like to understand the case of positive $\Lambda$ as well, but I have more modest ambitions.

Posted by: Jacques Distler on July 23, 2004 2:13 PM | Permalink | PGP Sig | Reply to this

Re: Taking Λ to zero

I am sure my personal ambitions here are way more modest than your’s are. :-)

But I do find it curious that Hawking starts off by saying

The question is, is information lost in black hole evaporation. If it is, the evolution is not unitary, and pure quantum states, decay into mixed states.

I don’t see any particular boundary condition at infinity mentioned here.

The fact that these play a crucial role later on in the talk is one sign of several that this talk is a little - strange.

At least we can conclude that now also Hawking acknowledges that AdS/CFT exists.

But, as you empahsized drastically, this is no news. If we could just be sure that the observed universe is asymptotically AdS QG were solved and all that remained was to figure out some details.

Posted by: Urs Schreiber on July 23, 2004 5:49 PM | Permalink | PGP Sig | Reply to this
Read the post Of Course Quantum Gravity Has Unitary Time Evolution
Weblog: Dichotomy's Purgatory
Excerpt: No Information Lost Here!Anyone who hasn't been asleep for the past 6 years knows that quantum gravity in asymptotically anti-de Sitter space has unitary time evolution.Well, duh....
Tracked: July 23, 2004 4:56 PM

Re: No Information Lost Here!

Well, thank you all for the explanation why real flat space is -really- different! Guess whose infinities hits in as ususal.

Also this comment from Serenus Zeitblom in sci.physics.research group helped: “…by the way, cf J. Distler, I suspect that
Hawking *does* regard the negative cc as a mere technicality.
Rightly or wrongly – I would say wrongly. And I’m quite sure
that he does not care about the Lambda -> zero limit. Why should
he? Either our world *really* somehow-or-other has a negative
cc, in which case there is nothing to worry about, or it *really*
has a positive cc, in which case all this, including the
zero cc limit is of little or no interest. Unless someone knows
how to show that the cc is *really* *exactly* zero…….”

So maybe I got that part right anyway.

Posted by: Torbjörn L on July 26, 2004 11:34 AM | Permalink | Reply to this

Re: No Information Lost Here!

Uuh, I mean the part about “Does one really need flat space, …” of course.

Posted by: Torbjörn L on July 26, 2004 11:43 AM | Permalink | Reply to this

Re: No Information Lost Here!

I’m pleased to say i haven’t the slightest idea what you’re talking about, but i will say that I routinely use the microwave to make quesadillas.

Posted by: jason on July 26, 2004 5:43 PM | Permalink | Reply to this

Re: No Information Lost Here!

I’m pleased to say I find myself in almost exactly the same position as jason, except for the unique addition of not knowing what a quesadilla is.

Posted by: Shiv on July 31, 2004 8:44 AM | Permalink | Reply to this

Re: No Information Lost Here!

If I recall correctly, a little over two years ago someone mentioned an experiment in Black Mesa back in ‘99 I believe that was based around string theory and the 7th dimension. The only reason I recall this is because he kpet rambling on about the number 7 and its origins. Then he babbled on and on about G Men. Crackpot. I think his name was Barney. Anyway, It was postulated that a black hole is the summantion of a simple string, which can be represented by placing a small weight on the middle of a rubber band and holding the ends of said band in your hands. The weight flexes back and forth in a basic pattern, but when done in the 7th dimension its effects are quite intriguing. I believe he called this experiment the “roshambo principle”.

Posted by: Gordon Freeman on September 7, 2004 1:39 PM | Permalink | Reply to this

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