Black Hole Information Loss Question

[Chalnoth]

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.

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.

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.

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 black hole.

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]

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 black hole.

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

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 black holes 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, Hawking 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]

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 black hole.

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

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]

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

Gravity travels at the speed of light.

 

[curiousOne]

Gravity travels at the speed of light.

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

 

[Chalnoth]

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

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]

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 ?

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]

By this you must mean that the position of the object has to become hidden because of Heisenberg's uncertainty principle right ?

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]

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.

It's not terribly simple, unfortunately, but if you want a thorough book on GR, see this text:
https://www.amazon.com/dp/0716703440/?tag=pfamazon01-20

 

[Mark M]

It's not terribly simple, unfortunately, but if you want a thorough book on GR, see this text:
https://www.amazon.com/dp/0716703440/?tag=pfamazon01-20

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.

 

[Lino]

... Anomaly cancellation arises when you consider moving bodies... 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...

Chalnoth, does this imply greater than c propagation of gravity, or is space-time warped to accommodate it?

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.

Mark, Can I confirm, are you referring to the lecture notes from '97?

Regards,

Noel.

 

[Mark M]

Yes, they're from 1997. They're a pretty fair introduction to the topic.

The text that Chalnoth mentioned is arguably the best resource ever written regarding GR, but it's a monster.

 

[Chalnoth]

Chalnoth, does this imply greater than c propagation of gravity, or is space-time warped to accommodate it?

Not at all. A better way to understand it is that the curved space-time moves along with the moving object, though if the object changes its acceleration, the space-time won't be able to keep up and it will emit gravitational waves instead.

 

[George Jones]

does this imply greater than c propagation of gravity

No. My attempt at a non-technical explanation (I probably have introduced some inaccuracies:

Newtonian gravity predicts closed circular and elliptical orbits. This prediction depends on the fact that Newtonian gravitational force is directed along the line joining the instantaneous positions of objects, like the Earth and the Sun. If Newtonian gravitational force weren't directed along this line, orbits wouldn't be closed.

As the Earth orbits the Sun, the position of the Sun, relative to Earth, changes. If gravity propagates at the speed of light, shouldn't the Earth feel (gravitationally) where the Sun was (according to the Earth) eight minutes ago, that is, shouldn't gravitational force be directed along the line that joins where the Earth is now to where the Sun was eight minutes ago? And if this is true, then, according to the previous paragraph, how can the Earth's orbit be a closed ellipse?

To answer these questions, I am going to talk briefly about the main equation of Einstein's theory of gravity, general relativity, G = T. Here, G is a geometrical quantity that depends on the curvature of spacetime, and T is a physical quantity that depends on the distribution and flows of mass and energy in the universve.

In Einstein's theory, gravity is a manifestation of spacetime curvature. If T depends not only on position, but also on flow of matter, then (by the equals sign) G, spacetime curvature, and (thus) gravity are affected by the velocities of objects. This feature is not present in Newtonian gravity.

As an example, consider a uniformly dense planet. According to Newton, the gravitational field of the planet is independent of the spin of the planet. According to Einstein, however, a planet's gravitational field is not independent of its spin. Spin puts the matter of the planet in motion, so different spins give different gravitational fields. To test this for the Earth, a satellite carrying gyroscopes has been put into orbit.

Back to the Earth and Sun. Form the point of view of the Earth, the mass of the Sun moves, and so, according to Einstein, this motion contributes to the gravitational field of the Sun. The field of the Sun depends on where the Sun is, and on how the Sun moves.

These two contribution's to the Sun's gravitational field, position and velocity, add to produce an "effective force" that *appears* to point towards where the Sun is now, not where it was eight minutes ago.

What happens if the Sun magically disappears? The Earth will continue on in its orbit for another eight minute under the influence of an "apparent force" directed towards where the Sun would have been. After eight minutes, the Earth realizes that the Sun isn't there, and stops orbiting the missing Sun.

 

[Lino]

Thanks all. Much appreciated.

Regards,

Noel.

 

[Naty1]

Leonard Susskind has a very interesting book for the general public...non mathematical : THE BLACK HOLE WAR
[My battle with Stephen Hawking to make the world safe for quantum mechanics] 2008

[Lots of interesting insights often from a somewhat different perspective.]

This book is about Hawking original claim that information is lost and Susskind's refusal to accept that premise. Hawking seems to have acknowledged Susskind was one of the first to realize the implications of 'black hole information loss. Susskind says he finally prevailed via the Holographic principle, ADS/CFT, although Hawking needed a different perspective to convince himself some years later that he was wrong. Susskind concludes the book with an Epilogue referring to 2002:

Roger [Penrose] [still!] maintained Stephen was right and he and Stephen continued to believe {that information was lost} ...I was surprised since ...as far as anyone who had been following recent developments was concerned, Matrix Theory, Maldacena's discovery, and Strominger and Vafa's entropy calculations had finally put the question to rest...In a press conference in 2004 Hawking [finally] announced he had changed his mind...I [recently] learned Don Page had a made a similar bet in 1980 [to Susskind's] ...on April 23, 2007, two days before I wrote this paragraph, Stephen formally conceded...[to Page] ...

There is a photocopy of Hawking's concession note to Page, signed via Hawking thumprint!

Susskind says further:

..Although the issue of whether information is lost in black holes...has now coalesced around a new paradigm,...I doubt we have learned all its important lessons. ..At the moment no one knows how to apply String Theory, the Holographic principle [and Maldacena's ADS/CFT correspondence in anti de Sitter space] to cosmic horizons...

Radiation, degress of freedom, and particle production associated with cosmic horizons has been the subject of several recent threads and ARXIV papers in these forums.

It turns out that entropy, [a subset of information theory] and particle production as well, can be associated with a variety of horizons, even the Hubble sphere which has not usually been thought of that way in these forums:

one such is here:

http://arxiv.org/abs/1207.0505
T. Padmanabhan, July 2012

and the discussion:
https://www.physicsforums.com/showthread.php?t=618397

...This bulk volume is taken to be the Hubble volume in which the enclosed bulk space is taken to be the cosmic space that has already emerged; The surface is the Hubble sphere. The emergence of matter [degrees of freedom] along with cosmic space occurs during the current expansion era when the universe is making the transition from one de Sitter phase to another.

and Ted Jacobson's foundational 1995 paper:

...That causal horizons {They don't have to be event horizons.} should be associated with entropy is suggested by the observation that they hide information. In fact, the overwhelming majority of the information that is hidden resides in correlations between vacuum fluctuations just inside and outside of the horizon...

Thermodynamics of Spacetime:
The Einstein Equation of State

 

[Lino]

Thanks Naty1. Another one for my reading list, but I think that I will bump this one up the list.

Regards,

Noel.

 

[Alex1]

Can someone explain to me what a tachyon is?

 

[Chalnoth]

Can someone explain to me what a tachyon is?

A tachyon is a hypothetical (and almost certainly impossible) particle that has negative mass squared. The negative mass squared causes the tachyon to have a speed which always exceeds that of light. As its kinetic energy approaches zero, its speed diverges to infinity. As its kinetic energy approaches infinity, its speed approaches the speed of light. These are probably impossible because if any existed and had any interactions at all with other matter, then they would basically cause the universe to explode.

 

[Alex1]

Haha Damn lmao that would suck good thing they don't. So basically the tachyon is really just a solution to an obsolete bosonic string theory?

 

[Chronos]

Haha Damn lmao that would suck good thing they don't. So basically the tachyon is really just a solution to an obsolete bosonic string theory?

No, it is a straightforward mathematical solution to the equations of special relativity. The notion of imaginary mass is not, however, as far fetched as it may appear. Imaginary currents are routinely considered in electrical circuits and the standard model of particle physics allow the Higgs boson, under certain conditions, to have imaginary mass. The biggest problem with tachyons entails logical parardoxes which can arise, such as the Tolman Paradox. These are normally considered mathematical artifacts with no physical analogue [i.e., unphysical solutions].

 

[Mark M]

Haha Damn lmao that would suck good thing they don't. So basically the tachyon is really just a solution to an obsolete bosonic string theory?

Like Chronos said, the tachyon isn't just a solution for bosonic string theories, but a general solution in relativistic quantum field theory. Tachyons themselves don't pose too much of a problem, but they imply an unstable vacuum, which would be catastrophic. Systems will prefer to be in states of lower potential energy. An example of this is a pendulum in a gravitational field. If you stand the pendulum up so that the mass is on top, then it has a lot of potential energy - slightly disturbing it will cause it to move to a lower potential energy state, e.g. fall over so that it is in a normal position.

If tachyons existed, then negative energy states would be possible. If so, then the vacuum wouldn't be the lowest possible energy state - and once you allow one negative energy state, you essentially allow then all, all the way down to infinity. So, the vacuum will rapidly decay into this state, which we obviously don't observe (you wouldn't be here if this happened). So, tachyons don't exist.

 

[Alex1]

Alright thanks man.

 

[Alex1]

Thanks man, that gives me a better understanding of a tachyon.