Black Hole Information Loss Question

[Ynaught?]

If I understand correctly, Hawking Radiation is created when the anti-particle of a virtual particle pair falls into a black hole while the particle of the pair escapes. The anti-particle goes on to annihilate with a particle in the black hole. Is not the annihilated particle identical to the real particle that escaped the black hole?

 

[Chalnoth]

Either the anti-particle or the particle can escape. It doesn't matter.

As for what happens inside the black hole, we can't say. All that we do know is that the particle that escapes the black hole carries with it some of the mass of the black hole.

 

[Ynaught?]

Either the anti-particle or the particle can escape. It doesn't matter.

As for what happens inside the black hole, we can't say. All that we do know is that the particle that escapes the black hole carries with it some of the mass of the black hole.

How does the escape of am anti-particle reduce the mass of a black hole? Such an event would have a particle falling into a black hole, thereby increasing the mass of the black hole and decreasing the mass of the rest of the universe.

 

[twofish-quant]

If I understand correctly, Hawking Radiation is created when the anti-particle of a virtual particle pair falls into a black hole while the particle of the pair escapes.

That's one way of looking at Hawking radiation, there are others.

The anti-particle goes on to annihilate with a particle in the black hole. Is not the annihilated particle identical to the real particle that escaped the black hole?

That's not quite what happens. What happens is that the energy from the gravity creates a particle/antiparticle pair near the event horizon. The particle falls in. The anti-particle escapes. Because the pair gets created from the energy of the gravitational field, some of that mass/energy of the black hole leaves via the anti-particle.

 

[Chalnoth]

How does the escape of am anti-particle reduce the mass of a black hole? Such an event would have a particle falling into a black hole, thereby increasing the mass of the black hole and decreasing the mass of the rest of the universe.

Annihilation isn't the cause of the reduction of mass of the black hole. It can't be, because if you annihilate two particles within the event horizon, the photons that are produced in the annihilation will have the same energy, and those photons will just remain in the black hole with no change in the behavior.

Instead, the particle that ends up falling into the black hole turns out to have negative mass (this isn't a problem for short-lived particles).

 

[Chronos]

It really does not matter which particle falls into the black hole, all that matters is the one that escapes has positive energy. Call it a quantum entanglement thing if that makes it more palatable.

 

[bill alsept]

Annihilation isn't the cause of the reduction of mass of the black hole. It can't be, because if you annihilate two particles within the event horizon, the photons that are produced in the annihilation will have the same energy, and those photons will just remain in the black hole with no change in the behavior.

So why do they talk about quantum fluctuations springing into existence and then annihilating each other? Are you saying that photons spring up out of nothing every time there is a quantum fluctuation?

Instead, the particle that ends up falling into the black hole turns out to have negative mass (this isn't a problem for short-lived particles).

Also wouldn't you think that a black hole would be accumulating far far more stuff than it could ever evaporate? It should continue to grow until there was no more space/universe to feed it.

 

[bapowell]

So why do they talk about quantum fluctuations springing into existence and then annihilating each other? Are you saying that photons spring up out of nothing every time there is a quantum fluctuation?

The actual picture of the Hawking effect in terms of virtual particles is actually rather murky. Hawking's original derivation made no mention of virtual particles slipping over event horizons; he instead examined the asymptotic transformation of a field fluctuation brought in from far away, past a black hole, and back out to very far away. If the initial field fluctuation far away was in its vacuum state, the final fluctuation far away generally is not (as a result of its gravitational interaction with the black hole). John Baez has a nice write up about this: http://www.weburbia.com/physics/hawking.html

The idea of the Hawking effect being the result of virtual particles popping into existence (and, yes, this could be e+/e- pairs popping out of the vacuum) near the event horizon, one falling in and one flying off, is more an illustration for the sake of popular science than an accurate description of the process, which admittedly, is hard to understand in terms of particles. After all, if there's any lesson we learn from playing with quantum fields in general relativity, the very concept of a particle has questionable significance in curved spacetime.

Also wouldn't you think that a black hole would be accumulating far far more stuff than it could ever evaporate? It should continue to grow until there was no more space/universe to feed it.

If the black hole is in a particularly crowded part of the universe (like hungry black holes at the centers of some galaxies) they will gorge themselves on surrounding matter and increase in mass. Only when there is little left to eat will they begin to incur a net loss in mass due to Hawking evaporation.

 

[Cosmo Novice]

Also wouldn't you think that a black hole would be accumulating far far more stuff than it could ever evaporate? It should continue to grow until there was no more space/universe to feed it.

Bill I have seen a few of your posts and just want to clarify something in case you were unsure.

At a distance beyond the Event Horizon of the Black Hole the gravitational effects are the same as any other body of mass, Black Holes are not hoovers that suck everything in. As a thought experiment: if the Sun were to turn into a black hole of 1 solar mass then the Earth would continue to orbit in EXACTLY the same way (except maybe a little colder!)

You may already know this but it seems like you may have this common misconception and I am just trying to help

 

[Chalnoth]

So why do they talk about quantum fluctuations springing into existence and then annihilating each other? Are you saying that photons spring up out of nothing every time there is a quantum fluctuation?

Yeah, pretty much. Though they can't stay around for long or else they'll violate conservation of energy.

Also wouldn't you think that a black hole would be accumulating far far more stuff than it could ever evaporate? It should continue to grow until there was no more space/universe to feed it.

If a black hole absorbs a negative-mass particle, it reduces in mass, which means it drops in size.

 

[bill alsept]

Bill I have seen a few of your posts and just want to clarify something in case you were unsure.

At a distance beyond the Event Horizon of the Black Hole the gravitational effects are the same as any other body of mass, Black Holes are not hoovers that suck everything in. As a thought experiment: if the Sun were to turn into a black hole of 1 solar mass then the Earth would continue to orbit in EXACTLY the same way (except maybe a little colder!)

You may already know this but it seems like you may have this common misconception and I am just trying to help

Thank you, actually I did realize that. It would be the same as if a mass suddenly turned into a star, the gravity would not change as long as the mass stayed the same. What I was saying had to do with Hawking's evaporation theory. I believe through the effect of gravity that all massive bodies are fed continuously. Even after all the visible surrounding matter has been pushed into the black hole, space is still filled with particles and energy. As I said before there would be far more going into the black hole than could ever evaporate. As long as there was any SPACE/UNIVERSE left. Of course this is my opinion and I'm just looking for feedback.
Thanks again

 

[Chalnoth]

Thank you, actually I did realize that. It would be the same as if a mass suddenly turned into a star, the gravity would not change as long as the mass stayed the same. What I was saying had to do with Hawking's evaporation theory. I believe through the effect of gravity that all massive bodies are fed continuously. Even after all the visible surrounding matter has been pushed into the black hole, space is still filled with particles and energy. As I said before there would be far more going into the black hole than could ever evaporate. As long as there was any SPACE/UNIVERSE left. Of course this is my opinion and I'm just looking for feedback.
Thanks again

The black hole will only continue to feed as long as the temperature of its surroundings are higher than the black hole's temperature. If we imagine a situation where all of the normal matter is gone, and we only have black holes, then the temperature in question is the temperature of the CMB. So once the CMB temperature drops below the black hole temperature, it will start to evaporate in net.

 

[bill alsept]

The black hole will only continue to feed as long as the temperature of its surroundings are higher than the black hole's temperature. If we imagine a situation where all of the normal matter is gone, and we only have black holes, then the temperature in question is the temperature of the CMB. So once the CMB temperature drops below the black hole temperature, it will start to evaporate in net.

I agree and always have that black hole may evaporate and I can understand how this could happen. All I have been suggesting is that a black hole will continuosly be fed as long as there is space, given it hardly a chance to ever evaporate.

 

[Chalnoth]

I agree and always have that black hole may evaporate and I can understand how this could happen. All I have been suggesting is that a black hole will continuosly be fed as long as there is space, given it hardly a chance to ever evaporate.

Again, it has to do with temperature. If the temperature of the space is lower than that of the black hole, then the black hole will emit radiation more rapidly than it feeds.

 

[martinbn]

As already said the explanation with particle antiparticle is only an analogy. In the original paper Hawking writes:

"One might picture this negative energy flux in the following way. Just
outside the event horizon there will be virtual pairs of particles, one with negative
energy and one with positive energy. The negative particle is in a region which
is classically forbidden but it can tunnel through the event horizon to the region
inside the black hole where the Killing vector which represents time translations
is spacelike. In this region the particle can exist as a real particle with a timelike
momentum vector even though its energy relative to infinity as measured by the
time translation Killing vector is negative. The other particle of the pair, having
a positive energy, can escape to infinity where it constitutes a part of the thermal
emission described above. The probability of the negative energy particle tunnelling
through the horizon is governed by the surface gravity K since this quantity
measures the gradient of the magnitude of the Killing vector or, in other words,
how fast the Killing vector is becoming spacelike. Instead of thinking of negative
energy particles tunnelling through the horizon in the positive sense of time one
could regard them as positive energy particles crossing the horizon on pastdirected
world-lines and then being scattered on to future-directed world-lines by
the gravitational field. It should be emphasized that these pictures of the mechanism
responsible for the thermal emission and area decrease are heuristic only
and should not be taken too literally."

 

[Ynaught?]

So Hawking's argument is that a black hole has a non-zero temperature and so radiates as a thermal black body. His justification is based in QM but with that caveat, "It should be emphasized that these pictures of the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally," as posted by martinbn.

John Baez took up the argument, as linked by bapowell, beginning with, "In 1975 Hawking published a shocking result: if one takes quantum theory into account, it seems that black holes are not quite black! Instead, they should glow slightly with "Hawking radiation", consisting of photons, neutrinos, and to a lesser extent all sorts of massive particles."

And ending with, "Now in fact when you do a Bogoliubov transformation to the vacuum you get a state in which there are pairs of particles and antiparticles, so this is possibly the link between the math and the heuristic explanation."

This leads me back to the original question, which was (admittedly) understated. If Hawking radiation is more than simply thermal (i.e. comprised of "photons, neutrinos, and to a lesser extent all sorts of massive particles") then should not an observer at infinity be able to (at least in principle) measure the properties of all of the particles emitted by the black hole?

 

[eloheim]

Yes sorry if this is just asking the same question again in a different way ...

I keep hearing that one of the big issues that is had with Hawking Radiation (or is it only a problem in relation to the Information Loss Paradox maybe??..) is that there is no mechanism for information to be transferred from the incoming B.H. food to the outgoing Hawking Radiated photons? I've heard it could be said that the two pass by one-another, but there's nothing suggestive of an interaction between them. Am I anywhere near on the right track so far?

And I guess if that's truly the question, anyone around here who might be capable of recounting the popular possible solutions would be great. I've seen that holographic theories may allow the intricacies of a B.H.'s event horizon's shape to preserve the information? Something like the shape of the (entire) horizon changes simultaneously with any incoming matter, and therefore exactly how the B.H. contacts the adjoining space around it (creating the vacuum gradient or whatever [you can probably tell how over my head I am here by now heh] that generates the radiation) can be effected by something seems unconnected. (And the key being the singular, integral nature of the B.H. I take it?)

Are there other ideas for a mechanism? Or just giving up on the problematic quantum information tenant?

Thanks

 

[Chalnoth]

Yes sorry if this is just asking the same question again in a different way ...

I keep hearing that one of the big issues that is had with Hawking Radiation (or is it only a problem in relation to the Information Loss Paradox maybe??..) is that there is no mechanism for information to be transferred from the incoming B.H. food to the outgoing Hawking Radiated photons? I've heard it could be said that the two pass by one-another, but there's nothing suggestive of an interaction between them. Am I anywhere near on the right track so far?

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]

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.

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]

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.

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]

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.

Where exactly has this been proven?

 

[Chalnoth]

Where exactly has this been proven?

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

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

 

[twofish-quant]

So Hawking's argument is that a black hole has a non-zero temperature and so radiates as a thermal black body.

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."

This leads me back to the original question, which was (admittedly) understated. If Hawking radiation is more than simply thermal (i.e. comprised of "photons, neutrinos, and to a lesser extent all sorts of massive particles") then should not an observer at infinity be able to (at least in principle) measure the properties of all of the particles emitted by the black hole?

Yes.

 

[twofish-quant]

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.

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]

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

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

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 Hawking 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]

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 Hawking 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.

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]

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.

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]

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?

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]

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

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]

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.

how does that curvature create the virtual particle pair?

 

[Chalnoth]

how does that curvature create the virtual particle pair?

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

 

[martinbn]

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

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]

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?

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.

 

[martinbn]

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.

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]

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