Black Hole Information Loss Question

martinbn

It seems that Hawking is saying more than that, not only that it gets out but he says something about how exactly it does it.

What I was (and still am) confused about, was whether there is a proof that information is not lost. Of course the problem is mine, I may simply have the wrong expectation when I hear 'proven' or 'paradox resolved'.

It would be nice to have a semi-popular explanation of Hawking's argument.

Chalnoth

Yes, absolutely. That's why it's a solution to the paradox. If black holes didn't seem to violate unitarity, there would be no paradox. Given some unitary laws of physics, it is certainly interesting how something like a black hole can conserve information. The glib answer that the laws of physics are unitary is somewhat unsatisfying.

Well, the really easy way to look at it is to consider a universe that starts empty, has a bunch of radiation come in from infinity to form a black hole at the center, a black hole which subsequently evaporates into nothing. Even not knowing what's going on inside the black hole, you can compute the information before and after the black hole forms, and you get the same answer, indicating the information is conserved.

Haelfix

I believe the current view amongst theorists, is that Hawking radiation and its quantum gravity based completions does NOT contain sufficient information to solve the information loss paradox, even in principle. Nor is the exact details of the 'local infalling observer' problem solved in the asymptotically flat case or even the AdS case. It is of course widely believed (and in the ADS case, proven explicitly) that physics must remain unitary, but how exactly that works concretely is an open question.

You really do need an extra physical mechanism or principle to solve the problem. For instance, some amount of novel nonlocal physics around the horizon of the blackhole.

In the initial formulation of the black hole complementarity principle by Susskind, he posited a sort of stretched horizon, which is essentially a brane that is formed close to the horizon. Upon further review, this doesn't quite work, but modern thought is that you need something like that.

Anyway, for a good discussion of the problem and why Hawking radiation perse cannot be the answer, see the following papers:

http://arxiv.org/abs/arXiv:1108.0302
http://arxiv.org/abs/arXiv:1101.4899

martinbn

Thanks, I'll take look at the papers. When you say "in the AdS case proven explicitly", what do you mean? Can you give me a reference?

Haelfix

So obviously if the AdS/CFT correspondance is exact, the unitarity claim follows right? Since the boundary theory is always unitary by inspection and the bulk is a theory of gravity and necessarily includes blackholes as states. In so far as that duality is concerned, there are various proofs that come in various degrees of rigor but it is still not ironclad, however I don't think any serious physicist believes the converse. It's been checked in too many different ways for it to go wrong at this point.

Also, Hawkings quasi proof in 2004 essentially works b/c it includes an arbitrarily small and negative CC as a regulator. So the claim I think is pretty well understood in the AdS case.

The flat and DeSitter case, obviously is far more thorny. At least for the former, the wide belief is that physics still remains unitary.

Now, what we don't understand (in any of the three cases) are the exact details on how this is accomplished locally. Even in the AdS case where we almost know for sure that globally the physics remains unitary, the exact local and microscopic details of how the horizon physics accomplishes this feat is just not properly understood at all.

Something quite drastic appears to be necessary (like the Fuzzball proposal, which includes highly nonlocal interactions) and it seems like it can't be something simple like having all the lost information stored in delicately scrambled correlations from the Hawking radiation.

PAllen

Wow, thankyou!! These are the first papers I've seen that provide a (to me) believable approach to a quantum solution to black hole problems covering large as well as small ones.

curiousOne

Why can't the observer get the information back by watching the gravity field outside the black hole ?


Either gravity travels at the speed of light or it doesn't.

Assuming it doesn't:
Can someone explain why information is lost ?
I think, any observer outside the horizon will be able to detect ALL of the information that is falling into the black hole because that information *eventually* affects the mass of the black hole, and the gravitation field outside the horizon.
Assuming it does:
Then the information should never escape, but then again neither does gravity, so, there should not be a black hole. That seems circular to me.

It think the paradox only exists because of the assumption that space (3d , 11D, 2D or whatever) is defined outside of information-interactions. The fact that the entropy of a BH is proportional to the surface of the BH horizon is only because we have no clue what the words surface, volume, mass and field really mean.
They're all defined in terms of each other and it's a circular argument to try to find laws that apply to one without the other.
Think about this really hard: Why should space even be defined inside a black hole ?
If not, then why would the BH have a 2d or 7D or 11D horizon ? Do you see the nonsense in trying to give the BH horizon a dimension, let alone a size ?
You can hunt all day for a symmetry that simplifies your equations but the bottom line, is that symmetry applies to geometries, which imply the existence of space and time.

Now, then why should space be defined inside the horizon ? Oh yes that book you throw in the BH - sure it's 3d when you throw it. Does a wave function make sense past that point ? It's not like the PDF can extend to infinity anymore is it ? Does it collapse ? Is passing the horizon like sealing the box to forever leave Shrodinger's cat alone ?
And my favorite question: Why should space be defined outside the horizon ? Really, have you ever measured space ? Or rather do you experience it through interactions ? Would that not solve the paradox ? Would that not solve the EPR paradox ? Would it also not relegate the Heisenberg uncertainty to a mere artifact ?
Really, did you ever ask yourself how light knows how fast to go ? (I know it's a childish question, on the surface). I don't mind postulating that the speed of light is a limit, for information flow - but the Lorentz transformation is as much a transformation of space as it is of time and speeds. Light has no more speed than space has dimension.

What is limited is the number of events one can observe before information interacts.

If you can accept space time is defined by interactions between bits of information, the problem is to explain why it looks 3d most of the time. But there are plenty of examples where mathematical objects in 2d can be used to represent 3d objects. Voronoi diagrams are such examples.

Chalnoth

Gravity travels at the speed of light.

curiousOne

Great. So how does gravity reach the horizon to cause the horizon?

Chalnoth

Well, the simple answer is that it doesn't need to. Understanding how all this comes together in detail is far from easy, but a small part of it can be understood from a property of gravity known as "anomaly cancellation". This is a property that arises in a rather different situation, that of moving bodies, but it may help to illustrate how the speed of gravity doesn't always cause things to behave the way you would naively expect.

Anomaly cancellation arises when you consider moving bodies. If you naively thought that gravity was just a function of the position of the object, and the information about that position propagated at the speed of light, then you might think that if you had a moving object, you might think the gravitational pull of that object would actually lag behind the object itself due to its motion.

But this isn't what you would find. You'd find that the gravitational pull would point pretty much directly at the true current position of the moving object, no matter how fast the object was moving. How can this be?

Well, it comes down to anomaly cancellation. It turns out that the gravitational field itself depends not just upon where the object is, but also, in General Relativity, depends upon the object's velocity and even acceleration. For moving objects, these additional velocity and acceleration terms serve to exactly cancel with the fact that gravity propagates at a finite speed, so that the gravitational pull points directly at the moving object. Well, not exactly: it only cancels the velocity and acceleration terms. It doesn't cancel changes in acceleration.

This may seem magical at first, but if you think about it a bit it actually has to be true, because General Relativity is a theory which still describes how the universe behaves whether you are moving or not. So if we take a prototype moving object, and simply move along with that object, then to us the object will actually be stationary. And we know what direction the gravitational pull has to be towards a stationary object: it has to be toward that object's center. Since this picture has to be equivalent to one in which the observer is moving with respect to the object (and thus the object will appear to be moving to the observer), this forces the force to always be towards the center of the object.

Granted, this is a rather different physical situation. But I hope it illustrates that it isn't quite so easy to think about the speed of gravity.

curiousOne

Thanks. That provides much needed clarification.
So, observing how the object that falls into the black hole alters the black hole's gravity should be possible ?

Chalnoth

Yes. But the information of where that object is has to become hidden as it enters.

curiousOne

By this you must mean that the position of the object has to become hidden because of Heisenberg's uncertainty principle right ?
I understand the exact time it meets the singularity must also appear to be 'never' from the point of view of outside the horizon, but using the 'anomaly cancellation' that should be possible. Otherwise, it seems we're trying to have our cake and eat it too. If I observe an electron fall into a BH, I never really see itfall in, but using the anomaly cancellation I should be able to observe exactly when it hit the singularity, even if their precise location from my frame of reference is 'somewere on the horizon'.
Why is this wrong ?

Chalnoth

No, not at all. It's due to the limited speed of light. If, for example, a rocketship falls into a black hole, then there is no way to ever know whether or not it fired its thrusters after passing the event horizon. Information would have to travel at faster than the speed of light for that information to exit the black hole.

curiousOne

Right, I understand that, but following the clear argument of anomaly cancellation, that gravity never 'lags' behind any moving object then surely, I should be able to determine exactly where the object is, even inside the horizon.
Perhaps someone should point me to some nice textbook on the workings of gravity, because I just don't understand how this could possibly work. I think even a simple 4 body model would give rise to propagation issues that would only be resolved in deterministic time and that alone would go against the basic principle that light is the fastest way information can travel.

Chalnoth

It's not terribly simple, unfortunately, but if you want a thorough book on GR, see this text:
http://www.amazon.com/Gravitation-Ph.../dp/0716703440

Mark M

I don't know if MTW is very good for a first textbook on GR (because of it's complexity). I think Sean Carroll's lecture notes are a bit easier for a beginner.