Black Hole Information Loss Question

Chalnoth

Well, no, the information of what enters a black hole is necessarily encoded in the Hawking radiation that leaves it. It's just that that information is so exceedingly garbled that it is in practice impossible to determine from the outgoing radiation what fell into the black hole.

eloheim

Ugh...So the paradox was that, before the idea of Hawking Radiation, it seemed like the quantum information of the ingoing matter was disappearing forever, but Hawking's discovery (if true) shows how it can reemerge, thereby satisfying the universal bookkeepers?

I've actually read (e.g.) the wikipedia entry on this, etc., but it's still confusing to me.

Chalnoth

Well, Hawking radiation is on very firm footing, and can be derived in a large number of different ways. Hawking radiation has also been observed in analog systems where we produce sound horizons (as opposed to the light horizon of a black hole). So basically, if black holes exist at all (which is nearly certain), they produce Hawking radiation.

With that aside, the picture you paint is largely accurate. The main issue, however, is that it was a long time between the discovery of Hawking radiation and the solution of the black hole information paradox. Early on, it was largely believed that Hawking radiation could not contain any information about what went into the black hole. This has since been proven false.

martinbn

Where exactly has this been proven?

Chalnoth

You can read about it on the Wikipedia page:
http://en.wikipedia.org/wiki/Black_h...mation_paradox

Basically it comes down to this proof by Hawking announced in 2004:
http://math.ucr.edu/home/baez/week207.html

twofish-quant

That's one argument. There are others. Some of them boil down to "if Hawking radiation didn't exist, then black holes would have zero temperature, and that causes problems with thermodynamics."

Yes.

twofish-quant

Also what has been proven is that Hawking radiation *could* contain information about what went into the black hole. Whether it does or not is another question, but it's one of those cool things in which "either way something weird happens."

There is a weird consequence to Hawking's solution. If you have information-preserving Hawking radiation with black holes, then you should have information-preserving Hawking radiation at the "cosmological event horizon." If that happens then the total information content of the universe stays constant which means that if you wait long enough everything nearly repeats. (i.e. in 10^10^120 years, we'll be having this conversation again and 10^10^120 years ago, we had almost the same conversation.)

http://arxiv.org/abs/hep-th/0208013

It's a paper called "Disturbing Implications of a Cosmological Constant"

martinbn

I looked at the wiki page but says it nothing about a proof. Only lists verious proposals, all of which have some problems, so they can hardly be considered a proof. I haven't read Hawkings paper, hopefully later today, but the wikipedia page says that it uses AdS/CFT correspondence. I thought that that is still a conjecture. Even if it is proven, and I just didn't know about it, it would imply something about black holes in AdS spacetime. How does that resolve the paradox in general.

Chalnoth

If you read about the discussion that follows, it basically has to do with the topological structure of the black hole. If the black hole's internal topology is nontrivial, then some of the information can "escape" to another space-time. If the black hole doesn't change the overall topology of the universe, then the information is necessarily conserved. I don't think it's reasonable to expect astrophysical black holes to ever have non-trivial topologies.

martinbn

I am sorry, which discussion do you mean? I was going to try Hawking's paper, but I discussion may be easier to follow. Alos does the argument rely on AdS/CFT?

Chalnoth

This discussion was in the lower part of the link I sent on this.

ryder

how does hawkings radiation differ from the energy released in a quasar?

Chalnoth

Hawking Radiation comes from the curvature of space-time at the event horizon. The light from a quasar stems from infalling matter being heated to extraordinarily high temperatures as gets closer to the black hole.

ryder

how does that curvature create the virtual particle pair?

Chalnoth

The curvature doesn't create the pair. It just separates the pair.

martinbn

Now, I've read it, but it doesn't help much. I still don't know if the argument relies on AdS/CFT and in what way. It seems that it does, but then since AdS/CFT is still a conjecture, it means that there is not proof yet. Also does it mean that this will (when/if AdS/CFT is proven) resolve the paradox for information loss in black holes in AdS spacetime, or is the argument for any spacetime?

Chalnoth

Well, as near as I can tell it's still good enough as a disproof, that is, it demonstrates that the statement that the Hawking radiation cannot encode the information about the stuff that entered the black hole is false.

But in the end, it's pretty trivial to say that if the fundamental laws of physics are unitary, then it cannot be possible for information to be lost.