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Black hole information paradox

  1. Mar 17, 2013 #1
    I watched this documentary about an argument involving information loss in a black hole, Stephen Hawking managed to wind everybody up by claiming information was lost and therefore broke existing laws of physics.

    Its an old recording so it may not be relevant anymore but one part of this argument has always puzzled me.

    I think it was eventually resolved something like this, all the information about everything that fell into the black hole was stored holographically in the event horizon and this information was carried back into the universe by Hawking radiation as it evaporated.

    My problem lies in the holographic information in the event horizon, it shouldn't be possible for the following reason. As a black hole's mass increases its event horizon expands. If information is stored in the event horizon then its traveling away from the singularity. The event horizon is supposed to be a point of no return.
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  3. Mar 17, 2013 #2


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    You'll find a discussion of the various proposed answers to this question on the Wikipedia page "Black Hole Information Paradox".

    EDIT: URL corrected! Thanks
    Last edited: Mar 17, 2013
  4. Mar 17, 2013 #3
  5. Mar 18, 2013 #4
    Does anyone know the equation that Hawking came up with? It related entropy to area of the event horizon, plancks constant, the speed of light, and Newton's gravitational constant. I've seen it before, just can't remember it.
  6. Mar 18, 2013 #5


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  7. Mar 20, 2013 #6
    There is no generally accepted solution to the black hole information paradox. On Wikipedia you'll see that all the proposed solutions raise other issues or are purely speculative. The paradox remains a conflict between two generally accepted theories.
  8. Mar 20, 2013 #7


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    Leonard Susskind is NOT going "like" you on facebook :smile:
  9. Mar 21, 2013 #8
    The information is not flowing from the singularity. It was stored in the horizon from the very beginning. You may imagine that when you fall into a black hole, the horizon "scans" you and stores the full information about you.

    The horizon in this picture is not spherical. Rather, it is wrinkly. It stores information about you in local displacements. It is only spherical on average. In fact, information of the object falling into black hole is stored in waves moving along the horizon, just like the shape of an object falling into water is stored in the waves.
  10. Mar 21, 2013 #9
    The horizon of a black hole is not a special place, according to general relativity. If the horizon "scans" you and stores the full information about you, then I'm being scanned right now, in my non-special place. With no evidence to support it, the idea is indistinguishable from science fiction, like the baby universe proposed solution on Wikipedia.
  11. Mar 21, 2013 #10
    It is special. It's the point from where you can not return. From your words one may deduce that the horizon doesn't exist at all.

    You can not locally detect the exact horizon position. But that doesn't mean it doesn't exist.

    In a sense, yes. If we are now falling into a black hole, or even if we are orbiting it (and we do), we are affecting the hole's horizon. We are in the process of "scanning". A part of our information is leaking onto the black hole surface.
    When we completely submerge under the horizon, our scan would be completed.

    It's all just a consequence of the fact, that our gravity affects the black hole's horizon shape.

    It's Susskind's idea, by the way.

    It will still take few more years before we start making experiments with actual black holes. Until then, the only thing we have is theory.
  12. Mar 21, 2013 #11


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    That's what I think kugbol meant by "the horizon is not a special place". You and others are saying that the horizon somehow "scans" objects as they fall through it. But how does the horizon know that it is a horizon? How does it know that it is supposed to do the scanning, if there is no way locally to detect the exact horizon position?

    This is a key issue with the "horizon scanning" proposal (which Susskind supports, but it's not solely due to him). The responses to it basically involve invoking some sort of quantum phenomenon that *does* "know" where the horizon is; in other words, saying that classical GR is no longer valid close to the horizon, because quantum effects become non-negligible there even if the classical spacetime curvature *is* negligible (which it is for a large enough black hole).
  13. Mar 21, 2013 #12
    That was an analogy, lol.

    The position of the horizon is an objective thing. You are either under the horizon or over it, for all observers. If you dive into a horizon, there's no reference frame where you didn't.

    It's the same for the equivalence principle. You can not locally distinguish between acceleration and gravity, but the gravity does exist, doesn't it? Earth generates it's own gravity and no reference frame can deny it. You just can't tell if you are falling on Earth when you are closed in a box.

    There's no need for any physical entity to do the scanning. The only thing you need to understand is: the shape of the horizon depends on the mass distribution around the black hole. When some massive object approaches a black hole, the horizon deforms. Think of it: the object has it's own attractive force, so a particle sitting on the very edge of the horizon is attracted by it. If the object were a little closer, the particle would be attracted a little bit stronger. So, it could escape the black hole. That means, it was not on the horizon. In fact, the horizon backs off a little bit when a massive object approaches it.

    Now, the key idea of Susskind: the horizon shape depends also on distribution of mass inside a black hole. When a massive object falls into a black hole, it gets a little bigger. Does it get bigger immediately, preserving its spherical shape? No, that would violate the speed of light limit. In fact, it gets a "bump" in the place where the object has fallen, just like a wave on water. The bump then flows all over the horizon and flattens. The hole becomes approximately spherical again, but the wave remains forever.

    The position of a horizon when viewed globally, depends solely on the mass distribution of nearby objects. But when viewed alone, it looks exactly like a fluid surface. It's not just an analogy. The equations of horizon evolution are exactly the same as for fluid surface dynamics. Honestly I haven't actually seen them, but Susskind say so.
  14. Mar 21, 2013 #13


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    This is all true, but it doesn't explain how the states of infalling objects get stored at the horizon.

    And for the same reason, you can't tell if you're at the horizon when you're falling past it. So how can your state get stored there? More precisely, why would your state get stored there, particularly, as opposed to anywhere else? Why isn't a copy of your state getting stored right now in the space you occupy? (Which it isn't, according to the model you're describing.)

    Yes, there is. This discussion might be better in the Quantum Physics forum, though, since the "scanning" is a quantum phenomenon. According to the model you are talking about, there is some quantum process at the horizon (actually in the "stretched horizon", a boundary layer that extends for a Planck length above the horizon) that makes copies of the quantum states of objects falling through the horizon. But why should that happen only at the horizon?

    I'm not sure where you are getting this from. It's not wrong, exactly, but it's misleading. The horizon is not a "thing". It's the boundary of a region of spacetime that can't send light signals to future null infinity. Saying that the horizon "deforms" is just saying that that region of spacetime has an asymmetric shape, at least for some period of time.

    Also, I think you are misunderstanding what happens to the horizon when a massive object is falling in; the horizon does not "back off" when that happens. It expands. The fact that the massive object pulls "upward" on an object close to the horizon is more than compensated for by the fact that the massive object is falling inward.

    It would help if you would give a specific reference; I suspect that you are misinterpreting at least some of what you're reading about this topic.

    Again, I think it would help if you would give a specific reference. I strongly doubt that Susskind has said what you're paraphrasing here, since it's wrong. When a massive object falls into a black hole, the horizon expands *before* the object reaches it.

    This is not entirely correct either. The horizon does expand asymmetrically at first, and the asymmetry does turn into waves. But the waves (gravitational waves) are radiated away to infinity; they don't stay on the horizon. The horizon does settle down to a spherical state (at least, in the idealized case where the infalling mass adds no angular momentum to the hole).

    There are, according to the quantum model that Susskind and others have proposed, wavelike quantum states in the "stretched horizon" (see above). But they don't make the horizon non-spherical or only approximately spherical. The waves are quantum waves; they are waves in Hilbert space, not waves in ordinary space.

    No, it doesn't. It depends on the massive object that originally collapsed to form the hole.

    Again, can you give a specific reference? I suspect you are misinterpreting what Susskind says.
  15. Mar 21, 2013 #14
    Susskind's idea applies as well to the border between the Pacific and Indian oceans. I can design my equation for the border such that a bump flows over that border when a ship passes through it. But if you conducted a physical experiment where my equation says the border is, to find information about the ship encoded in the border, you wouldn't expect to find any.
    Last edited: Mar 21, 2013
  16. Mar 22, 2013 #15
    Well as for what Peter said i would agree that logically the EH should expand a little when a massive body approaches it just like the water level rises when moon is close because two bodies with mass attract each other , I know that because I'm writing this from a laptop that just fell from the desk.:)

    Now maybe I'm wrong with this but does the information necessarily needs to be conserved just like a book put into a cabinet and then taken out again in the same state with nothing changed or maybe it is more like when you burn wood or any other material,the material doesn't disappear instead it is transformed into different states of matter like solid to gas and one chemical to another.
    But as long as speaking that information could be lost or is lost , well then the question goes can you pick up the smoke from the burning wood later and tell that it cam from an object that was round or rectangular or how big it actually was , I think you can't.
    Just as after thousands of years the original Chernobyl reactor with all the buildings and town around it may long be demolished and recycled but the higher levels of radiation may still be there as to a reminder of what was the original state of the system years ago before changes happened.
    What I want to say is that states are changing with time and under certain circumstances and the information is not always preserved in a classical way rather the consequences or the outcomes are determined by the input or by what was there so maybe the information or conserved only in that matter.
    As if you would throw a dog into a black hole you could not get a dog out if it even if there would be a way to dissolve one and stop it from being a black hole.Just like you take a cd format audio recording then decode and compress it to a mp3, you cannot get back the original quality from the mp3 as some of the data is lost , some is transformed and some is overlapped in places where the coding algorithm found that they can be overlapped.

    For information to be preserved at the event horizon aka scanned that would rather mean that the EH is some kind of a physical place full with information as basically information is a property of matter and cannot be without it.Like there is no mind without the physical neurological processes taking place in one's brain.
    Rather the EH is just the barrier after which gravity is so intense that (the point of no return) not even light cannot escape or the escape velocity is higher than c , so that in falling matter is just broken up compressed , changed (in terms of atomic structure) .

    To add to the general discussion not my personal thoughts the question would be, how does the EH scan and preserve something if it's not a physical thing itself rather a point or line or a border after which "we can't see" ?
    There is no Event horizon from the viewpoint of the black hole nor for the observer falling into one , it's just a glimpse for us , then how come it store something?Like information? It's not even a glimpse as there are no reflections either as the light before the EH hasn't "seen" what's in it and after it does we can't see it anymore nor the story it would have to tell so...
    Last edited: Mar 22, 2013
  17. Mar 23, 2013 #16
    The opposite. The horizon contracts when an object approaches it. It then expands when an object has fallen into it. You may call it a repulsive force if you wish.

    Imagine a world full of black holes. They are in such proximity one to each other, that they deform they own horizons. You can have a full description of that universe by writing down positions, masses and momentums of all black holes singularities.

    Thesis: You can restore the full information of the universe from the shape of all horizons.

    In other words, there is one-to-one correspondence between the set of all configurations of singularities and the set of all configurations of horizons. When you move one black hole into other place, it will affect other's horizons different way. You can restore the information of the shift by checking how all horizons changed shape.

    You may call it a coincidence, but the dynamics of horizons closely resembles fluid dynamics. When the singularities are moving according to Einstein equation, the horizons are changing shape like a fluid surface.

    Now imagine two colliding black holes. Their horizons will be severly distorted when it happens. After the two holes have finally merged, the horizon of the new big hole will not be still. It will be distorted as well.

    Thesis: you can deduce the whole past history of a black hole from its horizon shape.

    The spherical horizon of a Schwarzschild hole is a special case of a stationary hole that has existed from infinity and will exist for eternity. Any other black hole will have a different horizon shape. If you somehow get to know the exact shape of the horizon, you instantly know all the history of the hole, including the information about all objects that have fallen into it. Provided that the world is deterministic, you also know the future.

    Black holes of different shapes affect their enviroment different way. That means - the information about the event horizon shape leaks away of it, despite it may be hard to measure directly. Since we know that the horizon shape holds all information about the hole past, we deduce, that the information of objects that have fallen into black hole leak away from it.

    Now, let me repeat: You don't need the horizon to be a physical entity. You don't have to have any fabric that exists positively and builds the horizon. The horizon is just a place in the spacetime, with no special local properties. It has however special global properties. It is a border of a region of space, where you are destined to meet a singularity. It's the singularities positions that hold the actual information. The horizon only mirrors that information. But thanks to the mirroring, you can restore the information of the current, past and future (if the world is deterministic) configuration of singularities positions. This also allows you to fetch information about objects that have fallen into a hole.

    This is the solution to the information paradox by Susskind. When an object falls into a hole, you loose information about it, since it disappears from our universe. But the information is still held in the horizon shape. This way, the information is preserved.

    Yes, I mean - it depends on the objects that have fallen into the hole and the objects that are outside it. The singularity is also "near" the horizon.
  18. Mar 23, 2013 #17


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    No, it doesn't. Where are you getting your information from?

    No, their horizons will merge into one. It will not be a static situation.

    Reference, please?

    Is this something you just made up, or do you have a reference?

    Again, reference please?

    The singularities don't move. They are spacelike surfaces; i.e., they are instants of time. They are not locations in space. Where are you getting all this from?

    That depends on how the holes collide. If they started out with angular momentum relative to one another, then yes, the final hole will not be spherical; it will be oblate, because it's a rotating hole (i.e., a Kerr black hole, not a Schwarzschild black hole). But its shape will be exactly oblate; it won't be "distorted".

    Incorrect. Any system with zero angular momentum that collapses to a black hole will form a precisely spherical hole. There are many different possible systems like that, and you can't tell from a spherical hole which one collapsed to form it.

    Once again, where are you getting all this from?

    Incorrect. Where are you getting this from?


    No, it's the boundary of a region of *spacetime* that can't send light signals to future null infinity. That's the definition. The fact that there must be a singularity inside is an *additional* statement, that will hold if certain conditions are met. It is not equivalent to the statement that there is a horizon.

    Singularities don't have positions; they are spacelike surfaces.


    Once again, I think you are seriously misinterpreting what Susskind says. Can you give any actual references? If you can, do so. If not, stop making statements that you can't support.

    Incorrect. The singularity may or may not be "near" the horizon, depending on your definition of "near" and on how massive the hole is. Also, "near" in this connection means "near in time", *not* "near in space". The singularity is not a "place in space"; it is an instant of time.

    (Technically, if the black hole is rotating, it's more complicated than that; but you don't appear to even understand the idealized non-rotating spherical case, so there's no point in going into the further complications of the idealized rotating case. Most black hole physicists don't believe the rotating Kerr black hole interior is physically reasonable anyway.)
  19. Mar 23, 2013 #18


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    This logic only holds if the horizon is a "thing". It's not. It's a global phenomenon, not a local one. The reason it expands *before* an infalling massive object reaches it is that the infalling massive object is going to reach it. In other words, to know the exact location of the horizon, you have to know the entire future of the spacetime; you have to know all the objects that will fall into the hole in the future, and when they will fall in.

    In the first case, there is no change in entropy (at least in the idealized case where we assume that putting the book into the cabinet is perfectly reversible--in real life it wouldn't be because you would need to expend energy to move the book back and forth, which would increase entropy). In the second case, there is. When an object falls into a black hole, entropy increases, so it's more like the second case.

    However, when physicists talk about the "information loss problem" of black holes, they are talking about something different. In your second case, where a material burns, at the atomic level (at least according to our best current understanding) the process is completely reversible; if you could keep track of the exact states of all the atoms, you could reverse the process exactly and "unburn" the wood. (Of course, you would also have to make sure you did everything in a closed box so none of the atoms would escape.) The reason we say that entropy increases when the wood burns is that we *can't* keep track of all the states. But that doesn't mean the "information" is destroyed; it just means it's not accessible to us. I.e., the information is still there in principle, but for practical purposes we can't make use of it.

    When an object falls into a black hole, something different happens; when the atoms in the object hit the singularity at the center, they are destroyed, and all the information they carry is destroyed along with them. In other words, there is *no* way to reverse the process, even if you could keep perfect track of all the atoms' states up to the point where they hit the singularity. Once they hit the singularity, it's irreversible *in principle*, not just for practical purposes.

    At least, that's the classical prediction. However, in quantum mechanics there is something called "unitarity", which basically says that nothing like that can happen to a quantum system. So dropping a quantum object into a black hole and having it hit the singularity would violate unitarity. Physicists like Susskind believe that violating unitarity is a worse problem than violating classical General Relativity, so they believe that something must happen at the quantum level to prevent unitarity from being violated. The "scanning at the event horizon" model (that's not really a good name for it, see below) appears to be the best current hypothesis for *how* unitarity is preserved.

    Yes, this is one of the objections to the "scanning" model: how does whatever-it-is that stores the information at the horizon "know" that it is at the horizon? The alternative is that information is being "scanned" everywhere, not just at the horizon. I'm not entirely sure what the current position is on questions like this; see further comments below.

    But it isn't; at least, classically it isn't. Classically, spacetime curvature at the horizon can be as small as you like, for a black hole of large enough mass; and therefore the atomic structure of an object falling through can remain perfectly intact.

    One of the possibilities for resolving this is that there are quantum corrections to the classical behavior that become large near the horizon. In other words, when you add quantum fields to the spacetime, the horizon is no longer just a globally defined boundary; there is now actual local physics going on that makes the horizon seem like it's filled with hot gas, even to an observer that is freely falling inward. However, I don't think this possibility is widely accepted, since it is open to the same question as above: how does the quantum field "know" that it is near the horizon?

    Yes, as I said above, this is the question, how does whatever is storing copies of infalling quantum states "know" that it is at the horizon? I have read quite a bit of what Susskind and others have written and I'm not sure what their answer is.

    Yes, there is. The horizon is not frame-dependent. But there is no way to know exactly where it is without knowing the entire future of the spacetime, as I said above.
  20. Mar 23, 2013 #19
    In these forums we usually discuss absolute/true and apparent horizons. Susskind utilizes another, the 'stretched horizon' described below. Whatever is 'right' or 'wrong' Susskind says in his book that Hawking came to agree with him.

    Note the very interesting pg 434 claim!!

    I've posted the following before on this topic:

    Leonard Susskind, THE BLACK HOLE WAR (his arguments with Stephen Hawking)

    Black Hole Complementarity

    In this view, all the information ever accumulated by a BH is encoded on a stretched horizon...a Planck length or so outside the event horizon and about a Planck length thick. This is a reflection of the Holographic principle: all the information on the other side of an event horizon is encoded on the surface area of that event horizon....

    [pg 434] Of every 10,000,000,000 bits of information in the universe, all but one
    are associated with the horizons of black holes. [So if you can lose information via black holes, it a really,really,really big deal….]

    (p238) Today a standard concept in black hole physics is a stretched horizon which is a layer of hot microscopic degrees of freedom about one Planck length thick and a Planck length above the event horizon. Every so often a bit gets carried out in an evaporation process. This is Hawking radiation. A free falling observer sees empty space.

    (p258) From an outside observer’s point of view, an in falling particle gets blasted apart….ionized….at the stretched horizon…before the particle crosses the event horizon. At maybe 100,000 degrees it has a short wavelength and any detection attempt will ionize it or not detect it!

    (p270)…. eventually the particle image is blurred as it is smeared over the stretched horizon and….and the image may (later?) be recovered in long wavelength Hawking radiation.

    Here are two descriptions of horizons which I like:

    Two 'simple' ones first:
    from Roger Penrose:

    Mitchell Porter posts: [from a forums discussion]

    and another more technical description:


    The event horizon of a black hole is actually lightlike. This follows from it being a null surface, and you can even think of the event horizon as being "trapped light". “the EH is a null surface--more precisely, it has two spacelike and one null dimension.”

    PAllen & PeterDonis…… the event horizon is a 3-surface whose tangent space at each point can be given a basis that has two spacelike basis vectors and one null basis vector…the EH is not a "thing". It's just a boundary between two regions of the spacetime.,,,, The strictly correct way to state it would be to say "looking at the spacetime as a whole, as a 4-dimensional geometric object, this particular null surface is an event horizon"…..The technical definition of black hole event horizons cannot be satisfied in a closed universe. There is no infinity to escape to…

    I am unsure of the source for the following explanation...but I have seen multiple explanations which are generally similar:

    The technical definition of black hole event horizons cannot be satisfied in a closed universe. There is no infinity to escape to…

    An apparent horizon avoids the future dependency problem precisely because it forms later and is generally inside the true event horizon. By virtue of forming later and being smaller, it responds to events which are quasi-locally committed, and not to things like a star interacting with a black hole in the future…An event horizon's definition is not causal. It is a feature of a complete spacetime manifold, which is the complete history of some hypothetical universe.

    [] enclosed my additions

    For a collapsing [mass?] shell, the true horizon starts forming while the shell is still a little beyond its SC radius, and it starts at a point. The apparent horizon forms a little later, when the shell is at the point of no return, and it can jump [discontinuously] into existence at a finite radius. It is still true that there is no matter at the center and no singularity when the apparent horizon has formed….The event horizon doesn't exist for a free falling observer. This is the same as a Rindler horizon - it only exists for accelerating observers, not for inertial observers.

    In other sections of his book Susskind explains the stretched horizon and Hawking radiation in terms of STRINGS:....he envisions the stretched horizon as composed of strings and from time to time quantum fluctuations cause a section of a string to lump up..and these can break from the main string an escape...'radiation' is born.
  21. Mar 23, 2013 #20


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    Yes, correct. More precisely, there is no future null infinity in a closed universe that recollapses.

    The apparent horizon is local because it has a local definition: it is a surface at which outgoing light rays don't move outward. This is locally measurable. It has nothing to do with the apparent horizon forming "later" than the event horizon or being inside it; those are global features, not local ones. IIRC there are cases in which an apparent horizon can form outside the event horizon.

    I agree with the second sentence, but it doesn't imply the first. An event horizon is a causal boundary, like any null surface.

    The EH is a global feature of the spacetime; it is not observer-dependent.

    This is one way in which the analogy between the EH and the Rindler horizon breaks down. There are different Rindler horizons for different accelerating observers, so the Rindler horizon is observer-dependent. But in any given spacetime with an event horizon, the EH is the same for all observers.
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