Wheeler coined this phrase; it refers to the idea that it is possible to specify exactly the full nature of a black hole using only three parameters. They are:
- angular momentum
(You can add "position" and "momentum" to the list if you want to, but they're just telling you where the hole is and not how it behaves, as it were.)
What happens when something that contains information falls into a black hole? Is the information thereby effectively removed from the universe? Does the object's hair thereby get removed? Last I heard the notion of information destruction was controversial, but I'm not up on the field. Does anyone have more recent (non-destroyed) information that they could share with us? -- AndyPierce
means that non-rotating black holes have perfect spherical symmetry.
Doesn't everything that falls into a black hole contain information? -- KeithBraithwaite
The only thing I found (http://scienceworld.wolfram.com/physics/BlackHole.html
) was that:
"Black holes can pulsate, as was recognized by Press (1971). Over the next decade or so, the pulsations were shown to always be stable using perturbation methods."
Theories about what happens to information in black holes can be characterized by what they predict happens when the black hole has completely evaporated away through Hawking radiation.
Some theories suggest that a singularity will be left with all the information swallowed by the black hole. Which raises the question of what happens when two or more singularities collide and restart the loss of mass through Hawking radiation. This suggests that such singularities contain arbitrary amounts of information using a fixed mass.
Other theories suggest that the information goes into a separate universe.
Still other theories suggest that nothing happens because the information has been radiated away. The theory that used to be called SuperStrings?
(aka M-Theory) falls into this last category. It gives an account of black holes without singularities and without loss of information.
In M-Theory, all of the information that falls into the black hole is at the event horizon. Superstrings are energetic enough that they can encode this prodigious amount of information. The superstrings involved have both of their ends attached to a plane within which they can freely travel. When two energy superstrings collide, they cannot form a closed loop because they are wound in the same way. When an oppositely wound superstring falls on the event horizon, it meets some other superstring and forms a closed loop which then escapes the surface of the black hole.
So in M-Theory, information is never destroyed, it's just decomposed into its finest possible constituents. Like burning a house in a 10^N Kelvin (can someone supply the N) fire.
And then, just because BlackHolesHaveNoHair
doesn't mean they don't have interesting internal structure (unless M-Theory is right). Unfortunately, the only thing I can think of at the moment is super-inflated gravity.
...falls into...information...effectively removed...
The answer is yes. The information content is effectively destroyed. Just as the information content of a satellite is destroyed if you send it straight into the sun. -- HelmutLeitner
Not to a physicist. In a deterministic universe, if you could reverse time around the sun then the satellite would come back out of it. And cosmologists do tend to believe that the universe is deterministic. I like to think it's their job to better understand quantum reality than the run of the mill quantum physicist (see QuantumPhysics
- You can't reverse time, so it will never come out of the sun again. But I admit that such a realistic view (I was a theoretical chemist in a former life doing quantum and thermodynamical simulations) is less entertaining than speculative ideas. -- hl
- Even physicists like to entertain themselves. :)
Information includes all state information. Entropy is just low level state information and so a hot object has lots of information. A well-ordered (cold)object may have lots of high-level information but it has little low-level information (entropy) and on balance it has less information.
- Entropy and Information are different things. To throw them into a pot and stir won't lead you anywhere. Entropy is a thermodynamical concept, hard to really understand. The information content of a love letter won't change whether you read it at 300 or 310 Kelvin. -- hl
- The state information of a love letter will be higher at 310 kelvin, it's just that most of that information is heat which being bound to the lower physical level (instead of the higher abstract level of ink stains) gets filtered out by the human brain and so isn't perceived. Signal overload causes humans to perceive lots of information as no information. Information has the same properties and obeys the same laws as Entropy. You can describe thermodynamics in terms of information. The only thing I don't know is whether there is an analogue to the concept of Gibbs' free energy. Now, the everyday concept of information outside of InformationTheory is usually closer to lack of information than to information. The only thing you don't know, huh? :-)
- I hate to do nitpicking, but: information isn't heat, either. There is no kind of interaction or radiation that communicates the state information. State information isn't available anywhere. So it isn't filtered by the human brain.
- If you redefine thermodynamics in terms of information then you effectively say "everything is information". This may be true, depending on how you want to define your words, but: this doesn't solve a single thermodynamic problem and it deprives the word "information" from any useful meaning it might hold.
- There is no way to tackle these phenomena on a symbolic level by just using words as tools. Nobody can, sorry. -- hl
I think that explanations of InformationPhysics?
are in order. -- RichardKulisz
- I can't comment on them, because I don't know them enough. But if they tell you different about satellites or love letters, then they go wrong. Do they? -- hl
- Actually, I don't know enough about InformationPhysics? to explain well. You tell me. -- rk
- I'd prefer not to go into arguments. Let's enjoy our smalltalk. -- hl
Doesn't it need infinite amount of time (for us, hopefully not falling into a black hole) to see any object reaching the event horizon? -- NikitaBelenki
I don't think so. The event horizon is defined as that distance at which the escape velocity from the black hole equals or exceeds the speed of light. That's not the same as the distance from the hole at which an object falling into the hole reaches the speed of light (which it doesn't). Since objects falling into the hole have not reached the speed of light by time they get to the event horizon, their relative time dilation (relative to observers not falling into the hole) is finite, hence they do cross the event horizon in non-infinite time. (I think; again, physicists, a little help here?) -- AndyPierce
The slowing down of one's proper time near a black hole isn't due to acceleration of one's body towards the black hole but merely from one's presence inside a gravity well. That slowing down of time doesn't actually stretch to infinity. What stretches to infinite time (if it were possible) is the optical image left behind as you near the event horizon. It's all an optical illusion. And even as the image stretches to infinity, it gets infinitely dimmer.
Interesting black hole FAQ at http://skyron.harvard.edu/john/bh_faq.html
I found Black Holes and Time Warps : Einstein's Outrageous Legacy
by Kip S. Thorne, ISBN 0393312763
, to be an outstanding read, both for pure writing, interesting history and a catch-up on physics. He explains the difference between little black holes and big ones (in a little one, the delta gravity near the event horizon will tear you apart, but in a big one it won't... you'll never get out but will be quite comfortable for a while). -- AlistairCockburn
isn't right, objects genuinely don't cross the event horizon in the frame of reference of an external observer. It's only in their own frame of reference that they pass through and fall into the singularity. Space-time undergoes some odd changes near a black hole, and if memory serves, at the event horizon one of the spatial axes swaps places with the time axis, leading to such discontinuities.
You know this is all assuming that general relativity's version of black holes exist. As opposed to, for example, superstring theory's. And given that we know that GR must be wrong, ultimately, then I know which side to bet on.
I once read a very interesting book featuring all sorts of theories of what goes on inside black holes. Weird features like hyper-mass abounded. But when all was said and done, it was all crap because it depended on a theory we know to be wrong.
GR is incomplete
, but any better theory has to approximate it for large scales and low fields. When talking about divergence of frames near the event horizon, I would trust GR. When talking about what happens to information at the singularity, of course it's completely inadequate.
How you got from "large scales and low fields" to "event horizon of a black hole" is beyond me. When talking about anything going through the event horizon, I wouldn't trust GR at all. Further, it's not that GR is "completely inadequate" when talking about what happens "at the singularity" but rather that it's utter bullshit just for mentioning a singularity. You trust what's untrustworthy and you "mistrust" what's nonsensical crap. Those aren't signs of thoughtful judgement; more like knee-jerk celebrity worship.
- (A) GR is still a very good approximation (as tested by actual experiment) in other regions, so a future theory that replaces it will have to give essentially the same approximations in those areas (otherwise it wouldn't be a better theory), so that's not so different than any other theory that serves as an approximation even though later superseded, including Newtonian physics - which is still preferable in the domains where its approximations are good ones (like the dynamics of baseball).
- (B) Singularities are a problem in general, not just for GR. For instance, all experiments make it seem that electrons behave as point particles. But point particles lead to singularities either with Newtonian gravity or electrostatic attraction in classical physics. So although many would agree with you that GR is BS on the subject of singularities, it nonetheless is a mistake to think that this problem is in any way unique to GR.
I was under the impression that the event horizon of a black hole wasn't strong enough for string theory to make substantially different predictions as to the geometry of spacetime (or rather the four dimensional slice we like considering), beyond rounding out the discontinuity on a scale where quantum effects dominate. If I'm wrong in this, I would appreciate being informed, and knowing what the corrected version is. Of course it's completely inadequate
was intended to be read as the theory doesn't say anything coherent;
I'm sorry if that was missed. You could be a little more generous in your reading, though.
- No, no I really couldn't be more generous since if you'd bothered to read this page you would know what M-theory says about event horizons. Also, why should I bother to "interpret" a standard pat answer given to everyone, one you probably didn't put the least thought into? This is what M-theory has to say about black holes:
- there is nothing inside the event horizon
- the event horizon is a real object'
- anything that falls on it gets destroyed
- so nothing can fall through an event horizon, though lots of things smash into it.
Wow. As I said above, GR's description of a black hole from the frame of an external observer is that the space within the event horizon is effectively a separate universe and that things fall towards, asymptotically into, the event horizon and do not pass it. In other words, it's exactly
the same. So M-theory dispenses with the separate space-time within the discontinuity and terminates the frames of falling objects when they hit the boundary. Those do make sense, and I probably should have taken them into account. They're not radical changes enough to justify your claims that GR isn't up to this task, though, and they still don't justify your optical illusion bit.
Oh, and optical illusion is exactly right! You can't meaningfully talk about what an object does "in your reference frame" when you can no longer interact with that object at all. Even in GR, you can only talk about an object going through an event horizon from within that object's reference frame. Talking about it from your reference frame is BS. Like talking about something that's disappeared off the edge of the universe as if it still "really existed" within said universe. An object that's fallen through an event horizon has pretty much ceased to be part of the universe and this happens, at most, at the same rhythm as its image fading away.
I haven't said anything about objects that have fallen off the edge. What I said is that according to GR, objects don't
go through the event horizon in the reference frame of an outside observer - they stay
within its universe, and it can still receive signals from it (signals that approach zero in strength and become indefinitely close together by the clock of the falling object, but are non-zero nonetheless). So this complaint has nothing to do with what I wrote.
And yes, by the way, the infinite decrease won't actually happen in any quantum model, because small-scale effects will eventually become dominant. That doesn't provide any justification for the previous statement that there is
an infinite decrease, but it's of an optical illusion, which simply doesn't happen under any
You can't round-trip a signal to an object that's falling through the event horizon. One way signals aren't sufficient to demonstrate the reality of anything, only to infer it. And when your last image of something was just before its utter destruction, well that does put a different spin to it.
You can round-trip signal to any object that exists on this side of the event horizon, that's what makes
it an event horizon. If it took an infinite amount of time your time to be destroyed, it would be a real object in your universe for that long. As I said, this isn't actually quite what happens because it won't be destroyed at
the event horizon, it'll get destroyed once it's close enough to interact with stuff on it. But in that case the image disappears in finite time too. In any case, my main point stands: the slowing down of the clocks of objects falling in is not
an optical illusion, and they don't
pass through the event horizon.
Why would you spend so much time arguing to rely on superstrings over GR in a case where they give the same description
? All you had to do was point out that it dispenses entirely with the odd spacetime within the event horizon, something that isn't clear from the initial passage but does make sense, and I would have accepted that and corrected my reference to it, which was the only mistake in the above.
But they don't give the same description. I don't presume to either know or understand GR but I do believe that most people who know GR don't understand it, nor even know that they don't understand it. They merely know what formulas to recite at any given moment. And that's what gives me a leg up when I test their understanding.
That's likely fair, but appeals to superstrings wouldn't help those people. I like to think I'm not one of them, since I tend to think about it in terms of the geometry rather than the unenlightening equations, but you can form your own opinion.
Superstrings gives a unified picture of the universe down to every detail. Yes, T and R dualities mean that there are multiple formalisms for any one thing, but these formalisms are independent of the objects under consideration. You can envision the entire universe under one formalism, or the entire universe under another formalism, it makes no difference because the only difference resides in the symbols used to express what's going on. There is no way for the multiple formalisms to interact with each other except in the minds of human beings.
The "duality" of what happens to objects when falling through a black hole isn't like that. It's not a genuine duality that crosscuts the universe. Rather, it has a sharp boundary situated at the event horizon of a black hole. From the inside, it looks like you're falling through the event horizon with absolutely nothing marking the event. From the outside, it looks like you've gotten annihilated, destroyed, disappeared or whatever is currently in fashion. GR provides two radically different views of what's happening at the same location in spacetime depending on where you view the event from. To my way of thinking, GR is inconsistent.
But that isn't what GR says. The outside observer sees the falling object approach the event horizon, and its clock approach the collision time, asymptotically
. He doesn't have a different description for the collision with the horizon because by his clock, it doesn't occur within a finite amount of time. The only destruction he could see is that which takes place very close to the horizon, where quantum effects (which you do
need strings for) dominate. Meanwhile, if you imagine the object survived these, the passage would be marked by stopping and disappearance of the outside clock. There's no inconsistency, but there is
a sharp discontinuity between the spacetime on either side of the event horizon.
(The "duality" in "wave-particle duality" is another bogus duality and so complete BS. People would realize that if they cared about understanding rather than mere knowledge.)
Duh. And yet the concept survived how many decades in physics circles?
Since its inception. You're not the only one who isn't impressed with physics circles.
And that brings to mind the fact that GR ISN'T inconsistent. That GR DOESN'T support arbitrary reference frames without providing ways to reconcile them. In the twins paradox, SR produces multiple inconsistent views whereas GR unifies them by getting the two twins together again so we can actually compare which one aged less than the other. With the Mach principle GR does the same thing, there are solutions to GR where the entirety of the universe rotates, hinting that there is an asymmetry and that the Mach principle is wrong. So the same thing must be the case with falling into an event horizon. One view of it must be right and the other just a bogus illusion.
The relativity in General Relativity refers to relativity of acceleration / gravity. It does NOT refer to relativity of accelerated reference frames. And that is where your understanding of GR failed.
Either GR and the theory that used to be superstrings provide the same description of the universe, in which case you are wrong in talking as if there are multiple equally legitimate reference frames. Or you are right in your description of GR and GR is simply wrong.
This is entirely wrong. First, the twin paradox can be resolved by getting the twins back together in SR. In order to do this, one twin has to accelerate (or accelerate differently), and accelerated frames aren't equivalent. SR is what's left of GR when you use a flat spacetime and only look at linear paths through it, none of which are accelerating relative to each other. There isn't
any inconsistency, but it's a very limited theory.
You know, you haven't said anything that I don't know, you haven't said anything that I haven't already said, and you ARE contradicting yourself in the same paragraph.
There's no contradiction in twins who do different things ending up with different clocks. If you're already familiar with how the twin paradox works in SR, perhaps you'd like to tell me where the contradiction lies? Or are you assuming that working with acceleration means you're not SR, which isn't true if you let things change frames?
support arbitrary frames, but they aren't completely equivalent because their geometric properties impact the way they behave. The laws of physics aren't different for them when you consider them as paths through spacetime, but the space-only descriptions of the fields they experience will be different. A rotating object in a non-rotating universe acts exactly like a non-rotating object in a rotating spacetime, but certainly not much like a non-rotating object in a non-rotating spacetime. It violates Mach's principle, but only if you don't consider spacetime something that can have properties independent of the objects that inhabit it. Superstring theory take the same general approach.
The case of black holes has already been discussed. In GR, both the outside and falling frame are valid, but are entirely disconnected at the event horizon. This lasts until the falling object reaches the singularity, and GR breaks down. Around there, string theory would be necessary, except you've said it dispenses with the disconnected spacetime altogether.
So you really think that the fact there's an entire spacetime which exists in one reference frame but not another isn't an inconsistency between those two reference frames? I wonder what you would consider an inconsistency.
What you said originally: where something happens at a given point in spacetime according to one and not according to another, thus preventing any mathematical description that contains both. That doesn't happen here. If you wanted, you could jump through the event horizon and take a brief look at the second region, assuming you survived the passage. The superstring version, that you can't
and so there's simply a hole in spacetime, is incomparably better so I don't want to spend much time defending the older version. But they're both mathematically consistent, at least until you add on other structure.
I also don't understand what you mean when you say that superstring theory "takes the same approach" since it eliminates spacetime as anything but the emergent behaviour of strings. Unless that is what you mean by it.
That's exactly what I mean. In superstring theory, or any alternate quantum field theory for what they're worth, it's not surprising that the vacuum can have its own peculiar structure. It's interaction with that
structure that distinguishes frames from one another, rather than there being some inherent properties that allow some and not others.
I'm bowing out of this discussion because I think it's futile. I've put physics on the back burner 5-10 years ago and it's gonna stay there another 5-10 years. I don't believe there exists anybody who cares about knowledge enough to learn physics and about understanding enough to be able to explain it. The two are mutually exclusive values and the physics establishment is obsessed with providing absolutely ZERO understanding "for free". I don't envy any poor sap that tries to understand physics.
I just want to register my utter contempt for the standard pat answers in physics. Terms are thrown about without any concern for how misleading they are. GR's support of arbitrary frames is a prime example. You say GR does BUT blah blah, AND blah blah. Gee, do I really want to accept the simple universal statement when I can't understand any of the exceptions, conditions and modifiers? What do I care that GR supports arbitrary reference frames when you mean something by the term that I don't understand? It seems far more accurate to think that it does not.
I think what that means has been fairly explained. But more generally, I'm sorry and I sympathize. Information on relativity and basic quantum mechanics is generally equation-rich and understanding-poor, and for anything past that there's only useless newspaper soundbites. I should say, though, that if you don't understand something like how accelerated reference frames work in GR and aren't interested in an explanation, or aren't certain that they don't work and can't able to provide a counter-example, I don't see why you'd claim things about how it treats them. It doesn't seem like you from pages like QuantumPhysics
I'm not interested in an explanation
from you because I'd have been 98% certain
before we even started that you wouldn't be capable of explaining anything. As for now, after you're pulling this BS about how GR doesn't produce inconsistent reference frames because you could jump out of one frame to observe an event that only occurs in the other one, after you've pulled the BS that SR's reference frames aren't inconsistent between each other since you could reconcile them OUTSIDE of SR, well now I know that if I were ever interested in an explanation from you, I'd have to actively fight the misunderstandings it engenders. -- rk
Since none of what you just said bears any resemblance to what I said, I'd have to agree - trying to get an explanation from me while taking the most hostile interpretation possible of anything I say would be a waste of your time. Especially if you start insisting on using terms that don't belong in any proper explanation. That's not what I asked, though, I asked why you were making dramatic statements about something you yourself claimed not to understand. Other pages had led me to expect better. But whatever, the inexplicable hostility towards any statement I've made and total lack of any benefit of doubt suggests you're currently interested only in trashing physics-stuff, and that I should simply give. I'll do so, thanks.
I am extremely hostile to physics at the moment but especially to anything resembling classical physics. OTOH, you're getting a double dose of hostility due to the kinds of things you say. For example, the term "proper explanation".
Why would I take anything but the most critical, most hostile, interpretation of anything you say when I've already heard or read everything you've said at least a dozen times and none of it has shed an iota of understanding? To my mind, there's obviously something wrong with what you're saying and if I'm to engage you at all then it's my responsibility to ferret it out.
It wasn't my
idea to talk about classical physics, except that you
claimed it gave different results from superstrings in cases where it doesn't, and that it was inconsistent in places where it isn't. It wasn't my
idea to talk about interchanging frames fo reference, which are a terrible way to explain or consider relativity compared to what you've called the "block" universe - hence proper explanation
, i.e. one that's likely to make sense. The reason the above is all stuff you've heard in terms of unintuitive concepts is because it's all responding to things you said, claims you made while professing not to understand them. It has no relation to how I'd try and explain anything to someone genuinely interested in understanding or how I'd discuss with someone interested in helping me understand something. I apologize that nothing better came up.
- Have you read Superstring Theory by Green/Schwarz/Witten (ISBN 0521323843 ), or something similar? The Amazon reviewer makes it sound much more approachable than I used to think.
- Is that the "superstring bible"? I think I may have picked it up in the library (can't tell for sure without the cover image), and was completely lost. The sci.physics.research posts I've read have suggested not to even try to understand superstrings until you understand GR and particle physics. It looked like Greek to me, though the few symbols I recognized seemed to be grounded fairly strongly in GR. But you've got a better background than me in both abstract algebra and particle physics, so you might have better luck. -- jt
- Nonetheless I think the implication is that it is a difficult read, thanks for the feedback. My GR certainly should be stronger, and probably I should go back to renormalization groups, etc.
[Tangent moved to NeverMakeKnowledgePrerequisiteToUnderstanding
I once made a page here called physicsQuizOne with deep questions I would've liked to see answered. It got promptly deleted. Twice.
I only recall two of the questions. First I wondered how superstrings can wind around a dimension without self-intersecting and radiating away like cosmic strings. Second the term describing the winding energy of a string seemed to be the inverse of what they should be.
Does this phrase have any connection with "You can't comb the bald spot off a sphere"?
Wouldn't it be lovely if it were so? However, the inevitability of bald spots on spheres (and heads, for a suitably idealized definition of "head") is a consequence of Brouwer's fixed point theorem, which is a purely mathematical result.
All this discussion about the fact that an object does not fall into a black hole in finite time for an external observer looks completely pointless to me. As far as I understand, even the poor guy that is falling into the black hole will NEVER reach the event horizon from its very own point of view too. Why? Because as time goes slower from the outside to the inside, the times goes faster in the other direction. In clear, from the falling object's point of view, the entire universe goes faster and faster. The last things the falling object will see before reaching the event horizon will be the last moments of the universe, and speaking about what happens after the end of the universe is pointless. In short : nothing ever fallen and nothing will ever fall into a black hole.
I googlelized the question and I didn't find any convincing answser. Imagine I see somebody (A) falling into a black hole, but not very fast because the guy has thrusters that are slowing him down. I wait a little bit and then I send a friend of him (B) in the black hole again, but this time without any thursters. Will I eventually see B reaching A? If no, why? If yes, then A didn't cross the horizon by the time B started falling (because I could see A and B shaking their hands). -- PhilippeDetournay
The problem is that what you're seeing is an optical illusion that has nothing to do with the local reality of either A or B. In A's local frame of reference, A falls through the event horizon and smashes into the singularity. At least, it does in classical GR. In string theory, A smashes into the event horizon and vaporizes instantly. Whether B reaches A before the latter vaporizes, before A reaches the event horizon, is just an irrelevant detail.
It is not a detail: if I see A and B shaking their hands, that means that both A and B are able to send me information, and that information was sent after B's departure. Therefore A had not reached the horizon at the (A-reference) time B reaches him. This is not an optical illusion. As long as I'm able to setup an experiment that will make me receiving information from A, A has not crossed the horizon, optical illusion or not. So the question remains : when (in my time frame) won't I be able to get new information from A? If this answser is "never", and if I'm still able to send new information to A (new friends) until the end of the universe, then A will definitively see the end of the universe before reaching the horizon. There is a mistake somewhere, so please point it out :) -- PhilippeDetournay
As long as faraway observer O observes free-falling black hole explorer A, he'll see A [ignoring the Doppler effect, which will stretch out light emitted by A to incredibly low frequencies]. In other words, from O's point of view A will approach but never reach the event horizon. However, as A approaches the event horizon, O will see A's clock moving slower and slower. When O does the math, he'll find that the time on A's clock asymptotically approaches the moment in A's proper time when A perceives himself reaching the event horizon. So the only information O [a.k.a. the universe outside the event horizon] can receive from A is information that A sent before he reached the event horizon.
Here's the source of your mistake: from A's point of view, O's clock will continue to match his. O's clock would only appear to speed up if A were experiencing a gravitational force; since A's in free fall, he's not experiencing a force. To A, the universe will continue along sedately, even when he's inside the event horizon.
And that's why I call O's view of A (by which I refer to the perceived time dilation since I consider everything else an irrelevant detail) an optical illusion. If the time dilation were real, A would see the universe speed up and blue-shift.
I think your mistake is that you assume time dilation is symmetric: if A "slows down" (according to an observer), then the rest of the universe "speeds up" (according to A). That's not necessarily the case.
Quote: Imagine I see somebody (A) falling into a black hole, but not very fast because the guy has thrusters that are slowing him down. I wait a little bit and then I send a friend of him (B) in the black hole again, but this time without any thrusters. Will I eventually see B reaching A? If no, why?
[I assume that by "in the black hole" you mean "close to the event horizon". In Einstein's model of the universe, nothing within an event horizon can communicate with the outside universe.]
The answer to this question depends on how close A & B are to the event horizon when they meet. If they're far enough away that spacetime is still reasonably flat, then the answer is yes, you will see B reach A. Close to the event horizon, where spacetime is noticeably curved, the answer is no. The dividing line between "yes" and "no" in turn depends on other factors (A & B's distance from the event horizon when they meet, the mass of the black hole, & your lifespan). In the scenario you're probably imagining -- the meeting point extremely close to the event horizon -- the answer would be no. You won't see B reach A.
Imagine B has a strobe light which goes off every second (according to B). You keep track of when you see the light flash. When B is close to you, in a region of flat spacetime, your record will read 1 sec, 2 sec, 3, 4, and so on. As B gets closer to the event horizon, you'll start seeing a deviation: 60 sec, 61.00001, 62.00003, 63.006, 64.1, 65.4, and so on. That discrepancy will continue growing, until you're seeing a flash every few seconds, then every few dozen seconds, then every few hundred seconds, etc.
[The wavelengths of the light will be changing, too, but we'll ignore that complicating factor.] The time between flashes will grow tremendously, to months and years. Eventually, you'll die waiting for another flash from B. But the number of flashes the outside universe receives from B will equal the number of seconds (according to B's clock) it takes for B to reach the event horizon.
The information you receive from B will have been sent in that period of B's time (a finite, and likely short, duration from B's frame of reference), but it takes an outside observer asymptotically infinitely long to receive. The only question is whether you die before you see B meet A.
A's case is more interesting. Because A is not falling freely, to A the universe far from the event horizon will
speed up. The closer A is to the event horizon, the faster A sees time pass in the outside universe. If A applies extra thrust and returns to the outside universe, A will find that the "extra" time in the outside universe really has passed. B doesn't experience this because B is falling freely. According to B, his own clock will continue to match one in the outside universe. The difference between the two cases is A's acceleration.