Wednesday, May 30, 2012

Black hole information paradox flow diagram

I'm preparing a talk about the black hole information loss paradox. As I was thinking about a good way to summarize the vast number of attempts that have been made to address the issue, I thought a diagram would be helpful, and here is what I came up with. It's essentially a summary of the list in this earlier post. The red bars indicate the challenges one has to face in each case.

Do you find this diagram helpful, or is it more confusing? Have I forgotten something important?

Update: I've fixed a bug, thanks to Foresme's comment.


  1. Perhaps a portrait orientation of the page would make the flow more obvious. It took me a while to figure out that "Collapse of Mass" is where to start.

  2. What do you consider to be the key papers that have been published on this topic in the four years since your previous excellent summary?

  3. Hi Harbles,

    I see, good point. However, I assume I'll have a pointer. Best,


  4. What do you make of Unruh and Wald's arguments that there would be no infinite pair-production of remnants?

  5. Hi George,

    I agree of course. That's kind of the punch line of my talk. Though I don't know which argument you are referring to specifically - can you give me a reference? Lee and I, we had a quite general argument in our paper (see page 16). Best,


  6. I love it.

    There's so many bad infographics and flow charts out there these days that do little to elucidate complex problems and instead attempt to make banal concepts such as Are Cereals Really Good For You8?... well, I don't know why they bother.

    As a designer myself, I love the idea of taking complex physics problems and mapping them out visually.

    However, as a designer, I'm a little lost on this one. Forgive my ignorance but if the information does not come out in the Planck phase does it always create a remnant or baby universe and conflict with unitarity QM? Or might it go in one of those directions only? In the former case forking one "No" line may be more clear and if it's the latter case it seems like some sort of qualifier is missing to determine which "no" path to follow.

    Still, I think it's great and really compresses some complex ideas into a tight but clear structure.

  7. Hi Foresme,

    Ah, right. That doesn't make sense. I actually fucked it up. Looking again, on my notepad sketch it looks different, like this: Does the radiation come out in the Planck phase? -> No -> Remants or baby universes? -> Yes -> Infinite pair production problem. Respectively: Remants or baby universes? -> No -> Conflict with unitary QM. I'll update this later, thanks for spotting this. Best,


  8. What do you mean by "radiation at M>>T"?

  9. Hi,

    I just wonder if you are familiar with 2D toy models of QG in which this problem has been analysed. See for example hep-th/9402095 (and also gr-qc/9508009, hep-th/9606098). In these papers one has an explicitly unitary theory where information radiates away via nonlocal correlations.

    Your flowchart then hits the question: "How to make the semi-classical limit nonlocal?". But why do you expect that the semiclassical limit should be nonlocal? The nonlocality seems to come from quantum corrections, rather than the classical regime itself. As argued in those papers, QM is inherently nonlocal, so a quantum theory of gravity should be nonlocal as well (I'm oversimplifying here, but I hope you understand my basic question).

    That 2D toy model suggests that the classical limit is local, while the nonlocality (and thus information recovery from the BH) comes from quantum corrections. Therefore, why do you require nonlocality at the semiclassical level in the flowchart, to begin with?

    Of course, 2D =/= 4D, but nevertheless... :-)

  10. Hi Vmarko,

    Yes, I know the CGHS model. I can't say I'm terribly exited about 2d gravity though. Best,


  11. PS: I think you misunderstand my diagram. As I wrote, it's supposed to be a summary of approaches that have been tried for a talk I am preparing and the challenges that they are facing. I don't know how you read "my expectation" into this.

  12. Hi Rhys,

    I mean the temperature is much larger than the (remaining) mass. Or, in other words, you're far from the Planck phase. Best,


  13. "It's supposed to be a summary of approaches that have been tried for a talk I am preparing and the challenges that they are facing. I don't know how you read "my expectation" into this."

    Ok, let me rephrase --- why is the semiclassical nonlocality required in that particular branch (and thus considered a challenge for a potential model)? From the CGHS toy model one sees that the semiclassical theory is kept local, while only quantum corrections provide nonlocality. And this is all that is needed for information recovery. What exactly is the challenge then? Is there an argument that one cannot expect a similar scenario in 4D?

    My point is that "semiclassical nonlocality" is an overkill of a challenge --- nonlocality at the level of quantum corrections should be enough, according to the toy model. So am I missing something?

    Or, can you define what you mean by "semiclassical nonlocality" more precisely? Maybe I am misunderstanding something... :-)

    Btw, I really like the flowchart, it is great at encapsulating all approaches to the problem in an easy-to-follow manner.

  14. Hi vmarko,

    What is required is that in the semi-classical limit non-local correlations survive (and not just any such correlations but suitable ones). With semi-classical limit I refer to weak curvature. Sure, non-locality on the quantum level can do - but in addition you'll have to reproduce general relativity. In 3+1 dimensions. And with broken supersymmetry. For non-extremal non-static black holes. I'm not saying it can't be done. I'm saying that's the challenge to meet. And the CGHS model (which I believe we referred to extensively in our paper) doesn't convince me. Best,


  15. Bee, I'm wondering what you think of Marek Abramowicz's black hole research, particularly his ideas regarding the reversal of "centrifugal force" in the vicinity of a black hole?

    This theory, which I first ran across in Scientific American (, implies that an astronaut approaching a black hole in an orbiting space ship would, at some point, find himself in a whole new universe, with an inside-out space. The universe from which his space ship was launched would, from this new perspective, have been transformed into a black hole and the original "black hole" would be the gateway to the new universe.

    From this viewpoint, there would be no such thing as a black hole, only a kind of passage from one universe to another.

    When I read this it looked extremely promising, but it seems no one ever followed up on it, and I'm wondering why.

  16. Hi Bee,
    Very good chart. Only one thing missing that I can see and I suppose you might be including this in introductory remarks and don't show up here. That is: how do we define information? For instance, perhaps it is possible to define information flow as simply temperature change within a given preset volume. The tricky part is that to comply with GR it would seem that the flow of time would also change within that volume, since time and energy are duals of each other.

    Somehow it seems to me that it is being neglected that temperature itself is being neglected as a source of information. And of course in classical thermodynamics temperature is related to entropy but in my opinion in a not very thorough way. I think this may be the source of paradox of information loss in a BH.

  17. This comment has been removed by the author.

  18. P.S.
    Since time flow would change within a given volume as the temperature changes this might mean that information loss is only missing when looking at it from outside the special reference frame. In other words, from inside the reference frame the volume of space, as measured by the changing flow of time, would compensate for any loss of information that appears from the outside of the frame.

    One could specify the volume, as measured within the event horizon of the BH, as increasing during the accretion phase. In some sense this would conserve the density of information within the BH even while pulling in objects (information). During the dissolution phase in energy is radiated outward the the space within the event horizon would contract and would compensate for the loss of energy (again, information). The information density would again not change even as the BH completely evaporated.

  19. This doofus wants to know what "the dofs" means :)

  20. Great chart, Bee! My guess is that the answer will lie with non-local correlations = Yes.

    I've always thought that thinking of the vacuum |0> as randomly fluctuating is a bit of mistake, it is actually highly ordered. It is very hard to imagine a simple creation operator that can act on a highly disordered vacuum to produce a one quanta state.

    Yet, of course, an accelerated observer sees the seemingly thermally disordered Unruh vacuum. Just the state of motion produces what appears to be non-zero temperature and non-zero entropy.

    Therefore, the inverse is also possible. A state that appears to be at non-zero temperature because of geometry could nevertheless conceal sufficient order to allow for long-distance correlations.

    Of course, if I was right and if I could prove it, I would be a rich and famous physicist. Since I am not, I am likely wrong.

  21. Hi DocG,

    Never heard of that. Doesn't sound very plausible to me as a solution. This problem really isn't about what happens to some astronaut who comes to near a black hole, but what happens to the collapsing matter. Best,


  22. Hi Eric,

    I covered that in my earlier post. It doesn't matter how information is defined exactly, you can speak of a loss of information just because time evolution is not reversible. Best,


  23. Hi Arun,

    Yes, non-local correlations are a possible solution. I guess the one that's presently most fashionable. The problem isn't so much where to have the correlations, but how to get them. Consider you have that collapsing matter, which subsequently starts evaporating. How do you get the information about what it was constituted of into the matter? Just saying "non-local correlations" doesn't even touch on the problem. Best,


  24. "This doofus wants to know what "the dofs" means :)"

    It means "the doofus".

    No, it means "the degrees of freedom".

  25. Right, sorry for being somewhat cryptic - I didn't want too many words in the diagram.

  26. I'm surprised to learn you're not familiar with Abramowicz's work, Bee. He's a respected black hole researcher, with a long list of peer reviewed publications. See, for example:

    "This problem really isn't about what happens to some astronaut who comes to near a black hole, but what happens to the collapsing matter."

    Well, the "astronaut" is simply an aid to visualizing what happens when ANY matter is sucked into a black hole. What he's suggesting, as far as I can understand, is that the gravitational problem could fundamentally be a topological issue and he illustrates this by setting up a situation where, at a certain distance from the black hole's center, so-called "centrifugal force" is reversed, another way of saying that space is literally turned inside out.

    Under such conditions, a particle of matter drawn into a black hole would at some point find itself moving in the opposite direction, i.e., drawn into the universe, which would at that point itself appear as a black hole, with the original black hole appearing as a background universe.

    In other words, there would be no point at which the conditions you consider in your flow chart would actually apply. Thus none of the questions you pose would need to be answered, as they would no longer be relevant. :-)

  27. If I took a classical blackbody, and looked at a sufficiently tiny area of it, I would expect to see photons emitted as a Poisson process, and the spectrum of the photons given by Planck.

    Being thermal merely requires the Planck spectrum; perhaps information is carried away by a non-Poisson process of emission.

  28. Hi Bee,

    Of course mind maps are always nice....a shortened form of a complex issue.

    Strangely while one might of asked where to begin in map....what exactly is beginning, even though t is clearer that such indication draws the mind to it's location?



  29. Just to aid a bit an historical take may be an actually decidedly course of this is what became of seeing discrete values trying to be ascertained.

    This is the difference of a approach with regard to string theory? Hooft's transition to PI years ago helped me to understand this move.


  30. Hi DocG,

    As I said above, the problem I am talking about is not matter (books, astronauts) plunging into a black hole (or coming out in another universe), but the matter that formed the black hole to begin with. Are you saying there's something wrong with the singularity theorems? Is there something wrong with the interior Schwarzschild solution? Also, if that's the path you want to go, it gives you essentially a baby universe or a remnant. Best,


  31. I suppose what I'm saying is that, just as there is no edge of the Earth, beyond which matter would "fall off," there may be no center of a black hole, beyond which matter (either external or internal) would fall in, and thus no singularity in the usual sense.

    And yes, to me there is obviously something wrong with the singularity theorems and I say this not as a physicist (which I am not) but simply as a critical thinker.

    From what I've read sporadically in the literature over many years (and admittedly there is much I don't understand), it's all far too convoluted and complex to be convincing, with far too many entities and formulations to keep track of. Perfect for academics, since there are no end of dissertation topics to hand out, but not so good for those of us who have come to expect a certain degree of elegance in scientific thought.

    As Occam put it, "entia non sunt multiplicanda praeter necessitatem (entities should not be multiplied beyond necessity)."

    What Abramowicz has offered, it seems to me, is the possibility of approaching the problem in a radically new way, which is in fact both elegant and simple. His ideas are based not so much on quantum physics but relativity, both special and general, and, as he reminds us, general relativity is about treating gravity as a property not of matter but of space.

  32. Dear Bee,

    I was puzzled by your statement that you are not impressed by the results on black hole
    evaporation from the CGHS model, but then I realized by reading your paper with Smolin on the
    black hole information problem that you are not aware of my results on CGHS black holes.

    Actually, vmarko mentioned those papers in his post, and let me briefly summarise those
    results. CGHS model can be quantized canonically, and the Hamiltonian in an appropriate gauge is the one for free matter fields plus a nonlocal dof, which describes the gravitational
    sector and corresponds to a black hole mass. The evolution is manifestly unitary, and one can
    define the effective metric as an expectation value of the metric operator. In a coherent
    initial state, the effective metric can be evaluated perturbativelly, and the first
    correction (one-loop in matter fields) to the classical CGHS metric gives the Bose-Parker-
    Peleg metric, which describes an evaporating 2d black hole, with the correct Hawking
    temperature. This was the first demonstration that an evaporating (2d) black hole can exist
    in a manifestly unitary quantum theory. In the following papers it was shown that by calculating the 2-loop backreaction to the effective metric one obtains a metric which is free of curvature singularity, the Hawking radiation receives non-thermal corrections and the total emited Hawking flux is finite. This represents a concrete realization of option (3)
    from your paper with Smolin, although in 2d.

    In my CGHS papers it was also pointed out that there is a region around the classical
    curvature singularity where the metric operator has large fluctuations and hence a geometry
    is not defined in this region. This was the basis for the paper by Ashtekar and Bojowald
    (arxiv:0504029) where they used my CGHS results to propose an information paradox resolution
    in 4d. Hence the 2d model turned out to be quite useful, since it gave a possible scenario
    for an evaporating black hole in 4d.

    Best regards,

  33. Hi DocG,

    If there's no singularity for one reason or the other and matter travels to and persists in some other region of space, that's what is commonly called a baby universe or remnant, with all the problems that come with it. Best,


  34. Hi Aleksander,

    Thanks for the reference. Best,


  35. You forgot to include the violation of the holographic entropy bound by the remnants...

  36. I have a separate slide on this to emphasize the point.

  37. That figures...

    It's hard to forget the elephant in the room :-)

  38. "If there's no singularity for one reason or the other and matter travels to and persists in some other region of space, that's what is commonly called a baby universe or remnant, with all the problems that come with it."

    Not necessarily a baby universe, since all the black holes could be gateways to a single, parallel universe, the same "size" as our own, only (from our pov) inside out. Which could actually solve some problems.

    If it's inside out then it would also be manifested in the smallest things in our universe, i.e. subatomic particles. The strong force could actually be the gravity of our companion universe, only inside out, so felt more strongly by particles that are farther away from one another, etc.

    Also, if you read the S.A. article by Abramowicz you'll find a very compelling argument for a situation in the vicinity of a black hole in which space becomes so highly warped that it literally turns itself inside out! I hope you'll be curious enough to read this article and I'd love to know what you think of it, and if you can find a way around it. It would make for a very interesting blog post, if nothing more.

  39. Hi DocG,

    There are too many "would"s in your narrative. It is extremely implausible, in fact not compatible with locality and causality, that all the black holes would be gates to the same parallel universe. Best,




If the number of comments exceeds 200 you must click LOAD MORE at the bottom of the page to see all comments. This is also true for replies to threads. I know this sucks. Please complain to Google about this, not to me.

Comment moderation on this blog is turned on. Submitted comments will only appear after manual approval, which can take up to 24 hours.

Comments posted as "Unknown" go straight to junk. You may have to click on the orange-white blogger icon next to your name to change to a different account.

Note: Only a member of this blog may post a comment.