Tuesday, April 07, 2015

No, the black hole information loss problem has not been solved. Even if PRL thinks so.

This morning I got several requests for comments on this paper which apparently was published in PRL
    Radiation from a collapsing object is manifestly unitary
    Anshul Saini, Dejan Stojkovic
    Phys.Rev.Lett. 114 (2015) 11, 111301
    arXiv:1503.01487 [gr-qc]
The authors claim they find “that the process of gravitational collapse and subsequent evaporation is manifestly unitary as seen by an asymptotic observer.”

What do they do to arrive at this groundbreaking result that solves the black hole information loss problem in 4 PRL-approved pages? The authors calculate the particle production due to the time-dependent background of the gravitational field of a collapsing mass-shell. Using the mass-shell is a standard approximation. It is strictly speaking unnecessary, but it vastly simplifies the calculation and is often used. They use the functional Schrödinger formalism (see eg section II of this paper for a brief summary), which is somewhat unusual, but its use shouldn’t make a difference for the outcome. They find the time evolution of the particle production is unitary.

In the picture they use, they do not explicitly use Bogoliubov transformations, but I am sure one could reformulate their time-evolution in terms of the normally used Bogoliubov-coefficients, since both pictures have to be unitarily equivalent. There is an oddity in their calculation which is that in their field expansion they don’t seem to have anti-particles, or else I am misreading their notation, but this might not matter much as long as one keeps track of all branch cuts.

Due to the unusual picture that they use one unfortunately cannot directly compare their intermediate results with the standard calculation. In the most commonly used Schrödinger picture, the operators are time-independent. In the picture used in the paper, part of the time-dependence is pushed into the operators. Therefore I don’t know how to interpret these quantities, and in the paper there’s no explanation on what observables they might correspond to. I haven’t actually checked the steps of the calculation, but it all looks quite plausible as by method and functional dependence.

What’s new about this? Nothing really. The process of particle production in time-dependent background fields is unitary. The particles produced in the collapse process do form a pure state. They have to because it’s a Hamiltonian evolution. The reason for the black hole information loss is not that the particle production isn’t unitary – Bogoliubov transformations are by construction unitary – but that the outside observer in the end doesn’t get to see the full state. He only sees the part of the particles which manage to escape. The trouble is that these particles are entangled with the particles that are behind the horizon and eventually hit the singularity.

It is this eventual destruction of half of the state at the singularity that ultimately leads to a loss of information. That’s why remnants or baby-universes in a sense solve the information loss problem simply by preventing the destruction at the singularity, since the singularity is assumed to not be there. For many people this is a somewhat unsatisfactory solution because the outside observer still doesn’t have access the information. However, since the whole state still exists in a remnant scenario the time evolution remains unitary and no inconsistency with quantum mechanics ever arises. The new paper is not a remnant scenario, I am telling you this to explain that what causes the non-unitarity is not the particle production itself, but that the produced particles are entangled across the horizon, and part of them later become inaccessible, thereby leaving the outside observer with a mixed state (read: “information loss”).

The authors in the paper never trace out the part behind the horizon, so it’s not surprising the get a pure state. They just haven’t done the whole calculation. They write (p. 3) “Original Hawking radiation density matrix contains only the diagonal elements while the cross-terms are absent.” The original matrix of the (full!) Hawking radiation contains off-diagonal terms, it’s a fully entangled state. It becomes a diagonal, mixed, matrix only after throwing out the particles behind the horizon. One cannot directly compare the both matrices though because in the paper they use a different basis than one normally does.

So, in summary, they redid a textbook calculation by a different method and claimed they got a different result. That should be a warning sign. This is a 30+ years old problem, thousands of papers have been written about it. What are the odds that all these calculations have simply been wrong? Another warning sign is that they never explain just why they manage to solve the problem. They try to explain that their calculation has something in common with other calculations (about entanglement in the outgoing radiation only) but I cannot see any connection, and they don’t explain it either.

The funny thing about the paper is that I think the calculation, to the extent that they do it, is actually correct. But then the authors omit the last step, which means they do not, as stated in the quote above, calculate what the asymptotic observer sees. The conclusion that this solves the black hole information problem is then a classical non-sequitur.


  1. You've been complaining a lot recently about lack of quality papers in (what at least used to be) high-quality journals. Whatever happened to quality control?

  2. Quality control culls defective output to create quality. It fails. Quality must be assured. "Best efforts will not substitute for knowledge," W. Edwards Deming

    Rigorous derivation from (empirically questionable) postulates is enough! Cyclotron + perturbation treatment = synchrotron. Something is fundamentally empirically defective within physics. To criticize is to volunteer. Listen to the black swan in flight. Sitting in water is different.

  3. Phillip,

    Yes :( To be fair, the paper isn't actually bad, it's just that it is misleading in what it claims to have done. There is nothing new about the fact that the particle production process is unitary. The use of this particular method that gives rise to some time-dependence in the results has (for all I know) not previously been applied to this case - but then they don't explain very well what it means physically. I think the paper should have expanded on this and then dropped the claim that they calculate what the asymptotic observer sees, because this is just wrong. There are some other statements in the paper (about which state is mixed etc) that I think are wrong, but one could put this down as misleading or unfortunately formulated.

    In any case, this paper clearly doesn't belong in PRL, and certainly not under their new guidelines.

    Yes, whatever happened to quality control. Good question. What is maybe more interesting: Who cares that the statement in the paper is wrong now that it's published? In theoretical physics, there's no such thing as a wrong result. Have you ever seen any theory paper retracted? If it was an experiment, that's what they would have to do. If it's a theory paper, they can just put it down as an interpretation problem, and that's probably what will happen.



  4. Your argument certainly sounds right - the paper doesn't do what it say on the tin. I read about the functional Schroedinger picture once in Brian Hatfield's book, but this is the first time I've ever seen it used in anger, so the paper is good from that point of view!

  5. Sabine,

    I thought we clarified the issues over the emails. You downplay the main points of the paper, cling to one grey issue, and then trash the paper. I do not think that you are doing service to anyone here.

    We did not claim that we resolved the full information loss paradox. We just claim that the complete density matrix is that of a pure state. Since most likely there is no singularity at the center after you include quantum mechanics, like shown in many places e.g. Phys.Rev. D89 (2014) 4, 044003, then you do not trace over the modes that would have hit the (now non-existent) singularity.

    Then non-singularity plus our result that the subtle corrections to the diagonal terms purify seemingly thermal density matrix, completely resolves the information loss paradox.

    Do not blame the PRL referees and Editors. We made clear to them that we did not resolve the full issue. But they saw an important step forward toward the resolution. And a new unusual angle.

    Best wishes,


  6. "The original matrix of the (full!) Hawking radiation contains only off-diagonal terms, and no diagonal elements..."

    Am I misreading you here? A valid density matrix must have trace one, and thus, can't have 'only off-diagonal terms'...?

  7. Dear Sabine,

    Problems such as this will be addressed when micro black holes are produced at the LHC during the summer.

    I do not understand why you are so adamant that there will not be black holes at the LHC. You have recently stated:"I gracefully got out of this when it became obvious there wouldn't be black holes at the LHC, some time in 2005."

    In fact, as you are aware, according to certain additional dimensions scenarios, there could well be micro black holes at the LHC. I, for one, predict that there WILL be black holes at the LHC, based on my calculations. If you are interested I could explain these to you.

    Please prove to me why there will not be black holes at the LHC, because I disagree!

    Best regards,


  8. Sabine you say:

    “The authors in the paper never trace out the part behind the horizon, so it’s not surprising the get a pure state. They just haven’t done the whole calculation.”

    I’m a little confused. I assume the density matrix they deal with must be the density matrix of the outgoing Hawking radiation (i.e. the one that is perceived by the external observer) and the trace out has been implicitly performed.
    This density matrix represents a mixed state exactly because of the entanglement between the outgoing Hawking radiation and the particles that fall behind the horizon.

    Now, since presumably they assume that the BH evaporates completely, if they have shown that by the end of the evaporation process (before Planck mass limit is reached) this “outgoing” density matrix represents a pure and not a mixed state then indeed they have solved the paradox.

    This would mean that that the corrections to the correlations of the outgoing Hawking radiation with whatever is behind the horizon are significant enough to transfer the “would be lost information” to the external observer.

    Of course I have no clue if indeed they have shown that; it would be a big deal if they have.

  9. This comment has been removed by the author.

  10. Hello

    The first thing that comes to mind was that Mersini-Houghton showed, although with considerable criticism from Unruh, that the Hawking radiation emitted from gravitational collapse prevents the formation of a black hole.


    It seems these guys merely carried out a computation in a system where a black hole isn't formed in the first place. Thus no information loss problem to begin with.

    Just a thought. Cheers.

    Morgan H. Lynch

  11. Dijan,

    This was one of the more difficult blog posts to read (for me) for the content as well as the critique.

    In the conversation between those whose making a living depends on such ideas and experiments (including publishers who we assume try to state the case to other physicists and the public - I mean if they could be totally sure of an idea would they need any other physicists? Who then is the peers and how do we measure that if something is beyond observation right or wrong particles arise by natural process or vague creativity?)

    If, as you say, she has trashed your paper (if that matters, I mean my world does not depend on ideas like this for a living... and if they did I would not much care) I would be quite honored to be so trashed or have such input.

    A new angle? I find that an odd use of the common phrase in the wider scope of the problem... and is it new, or a good step to what is already given in nature to discover?

    I like this approach very much as some of it near some of my concerns- but I see where it has not solved some needs further principles (or mathematical methods) something to defend I suppose, but by further exploring heretofore unknown methods or general principles (perhaps we do not need the idea of antimatter ultimately if one could explain why the situation is not symmetric).

    What could be more insightful and helpful than this position (...paper should have expanded on this then dropped the claim...) Indeed, what is this unitary view on something asymptotic in freedoms or observations... it is a question beyond the simple one of quality vs quantity... it asks, finally, where is it outside the box (and something felt wrong in how we now do physics) does the meaning and interpretation go, if anywhere, and if the world makes sense, at least for a very wide span of our daring perceptions

  12. I can't express any judgement about the paper as my physics understanding is too low, but I like a lot the approach of the authors..

  13. Jochen,

    Thanks for the correction, you're right - I was talking about a different matrix (the one I called V in this paper) because I prefer to work with it. In any case, my point was just that the full state is of course not a mixed one. Best,


  14. Hi Dejan,

    Yes, I took into account our email exchange. Exactly what did I write now that you think is incorrect? I didn't "trash" the paper, I simply said you're not solving the black hole information loss problem, even though you say you did. Best,


  15. Morgan,

    The paper discussed here has absolutely nothing to do with the Mersini-Houghton paper which, besides this, is also wrong. Best,


  16. Giotis,

    What I am saying is exactly that the matrix they deal with is NOT the matrix of the outgoing radiation, but that of the full radiation, including the part that eventually gets destroyed. Dejan, btw (see comment above), who is the 2nd author of the paper, agreed on this. Best,


  17. Darius,

    Of course I cannot 'prove' that there will not be black holes at the LHC, I just told you that I don't believe there will be and that I didn't want to waste time on it. Interestingly, I wrote a piece over Easter on the question of 'belief' in theoretical physics that touches on this point, maybe I'll post it the next days or so. Best,


  18. Sabine,

    Thanks for your response.

    Firstly, you have inspired me to start a physics blog, please see here:


    I believe, in fact, I predict there will be black holes at the LHC. My colleague also hopes there will be micro black holes. Why? Because micro black holes could possibly prove to be a source of clean energy for the future (by accessing dark energy).

    In any case, I look forward to reading your future posts especially on the role of belief in physics.

    Einstein wrote profusely about the role of belief in physics. And I think it was Planck who said that "Above the entrance to the temple of science it is written 'Ye must have faith'".

    I look forward to your comments.

  19. " In theoretical physics, there's no such thing as a wrong result. Have you ever seen any theory paper retracted?"

    It depends on the definition of "retracted". First, if a theory makes a falsifiable prediction and it is ruled out, or if an experiment doesn't find what some people hoped it did, then there is no reason to retract anything. But I'm sure this is not what you mean. Rather, you mean the analog of an experimental paper where a mistake was noticed which invalidates the result.

    It does happen. One that comes to mind is this erratum. (This is a link to the full paper, which is less than a page. By coincidence, it also involves black holes.) Printing an erratum which points out that the main result of a paper is invalid is more or less a retraction. OK, this is not pure theory, but a "simulation" paper---but not experiment or observation. I particularly like the acknowledgements; I wonder how many hours of Axel's work they represent? (By another coincidence, a) Axel is also from Germany and ended up in Scandinavia and b) he's probably not far from you right now. Like myself, he started out in astronomy as a student at the Hamburg Observatory.)

    Another example is the infamous Bogdanov affair, where the editors of Classical and Quantum Gravity essentially retracted a paper; the statement is reproduced about two-thirds of the way down in John Baez's summary.

  20. Phillip,

    Ok, I stand corrected, it has happened twice in the history of physics ;) No, I didn't mean that a hypothesis was falsified, that's a normal scientific process. I meant exactly this: that a claim in a paper was just manifestly wrong, known to be wrong already at the time of publishing, and that claim should be removed from the literature. It's another thing if there is a difficult calculation that later turns out to be wrong. Of course this can happen. There are many examples where people have debated different results in the literature back and forth until they finally agreed on one. But this is not what I mean. I just mean something that is obviously wrong already at the time the paper appears.

    There is some flexibility of course how you treat something like this, but you see my issue with this case in particular is the following: The correct summary of the paper would have been "We repeat the standard calculation for black hole evaporation by a different method and find the same result." This would never have gotten published in PRL.

    The only reason this thing got published is that they claimed they solved the bh information loss problem (that the asymptotic observer sees a pure state), which is wrong. Now, you can see that Dejan is downplaying this. He and his collaborator (who I don't know) might indeed have thought that this was a new finding that the (full) radiation matrix is pure. Regardless of whether they believed what they wrote or whether they just lied, it is wrong, and if it had been right, there is no way PRL would have published the paper, certainly not with their new guidelines (see here).

    So what this looks like in my eyes is cheating your way into a high-impact journal. Of course the editor is to blame for this too, but my point is that the way theory papers are treated right now, once your stuff got published, it's basically untouchable and it doesn't matter whatsoever whether it's wrong or not. That, imo, significantly contributes to the decrease in paper quality because people figure they can just try and hope to get lucky. Best,


  21. Darius,

    Great that you set up your own blog and I wish you much success with this! I don't have anything to comment, except possibly that "hope" isn't the same as "prove". Best,


  22. Bee, the standards of PRL have gone down and lots of
    junk gets published in PRL
    I am amazed how whole bunch of upper limit papers which get published in PRL including searches for rare particles/processes which probably are not true/don't exist (such as proton decay searches, magnetic monopoles, Q-balls etc)

  23. Sabine,

    Only to add that it is my colleague who hopes that there will be micro black holes at the LHC, whilst I have the proof that they will materialise.

    Best regards,


  24. "whilst I have the proof that they will materialise"

    How about a public bet with a realistic but appreciable pay off? EUR 10 thousand?

  25. Dear Sabine,

    The problem is in the way you wrote your blog entry. Information about the paper that you try to review is completely lost in your writing. In that sense, your blog entry is worse than a black hole . The title and all the key points that you emphasize are highly misleading. In between the lines you barley mention the true message of our paper, but that of course gets lost in the noise.

    Look at our title: “Radiation form a collapsing object is manifestly unitary”. Where do you see the word “black hole”? Scan the whole paper and see that we never use the word black hole to describe what we are studying. The main point is that gravitational collapse produces radiation that has Planckian distribution. You calculate only the diagonal terms, i.e. produced particles, and you think the radiation is thermal and density matrix is that of a mixed state. But then you calculate the off-diagonal terms, i.e. correlations between the particles, and you see that the full density matrix is actually that of a pure state. Take home message: corrections can unitarize thermal radiation. Note that there is currently an ongoing debate about whether this is possible or not. This question has not been settled down. Just answering this question is enough for a PRL.

    As you noticed, great majority of papers on the topic deal with particle production is asymptotic static space-times. Treating the same problem with a new time-dependent formalism that has many advantages with respect to the standard one also merits a PRL.

    Finally, implications of our paper about the information loss paradox. What we have resolved in this particular paper is only one aspect of the information loss paradox. But a very important one. This is why we did not title our paper “solution to the information loss paradox”. But then you combine it with our previous results mentioned above that the singularity at the center is most likely erased with quantum mechanical effects, and now you can apply our new result to the context of black holes. This addresses the full information loss problem. Of course, you may refine the problem further, like what would an infalling observer see during the collapse (is evolution unitary for him), and that is the current topic that we are working on.

    This is the information that I gave you in our email correspondence. However, this information is completely lost in you blog entry.

    Best wishes,


  26. Dejan,

    You write in your paper, first paragraph (I am leaving out citations)

    "One of the most pressing problems in modern physics is the information loss paradox in black hole physics. Since Hawking radiation is purely thermal, it is possible to convert a pure state into a mixed state, which is forbidden in unitary quantum mechanics. It was often argued that subtle correlations between the emitted Hawking quanta which are usually neglected could be enough to recover information about the initial state and convert an apparently maximally mixed thermal state into a pure state. This point of view
    was also often criticized by noticing that small corrections to the leading order Hawking terms are not enough
    to recover unitarity. The purpose of this paper is to
    perform explicit calculations which may clarify this issue.
    We find indeed that the process of gravitational collapse
    and subsequent evaporation is manifestly unitary as seen
    by an asymptotic observer."

    In my reading you are saying here that the asymptotic observer sees a 'manifestly unitary' black hole evaporation, and that you have demonstrated this in the rest of the paper. Which, however, you have not done. You further raise the impression that you are demonstrating that correlations in the outgoing radiation are large and that solves the issue. Which, again, isn't what you have done.

    You write in your comment

    "But then you calculate the off-diagonal terms, i.e. correlations between the particles, and you see that the full density matrix is actually that of a pure state. Take home message: corrections can unitarize thermal radiation. Note that there is currently an ongoing debate about whether this is possible or not."

    No, there is no debate. Who do you think ever questioned that entangled pairs are a pure state? Did you actually read my blogpost? The FULL radiation is always a pure state. Nobody ever debated that. You just showed what everybody knows anyway. The debate is whether the state is still pure after you trace out the inside.



  27. If we add a single atom to black hole, then the black hole will become heavier by just a single atom. How the information about this atom couldn't be preserved, after then? Why we have so many discussions about it? I'm not a robot.

  28. Dejan,

    A question:

    In your formalism it’s not clear to me when exactly the information starts to leak outside of the horizon.

    As I understand it you must compute the corrections when the entropy of the black hole is reduced to half and then the information can come out.

    But I’m not sure if you have done that.

  29. Dear Giotis,

    We did not take back-reaction into account. The mass of the collapsing object is fixed. But the point is that correlations grow with the number of excited modes. As the beginning, they are very small, but then they grow, as can be seen from the graphs in the paper. You can see that the correlations become of the order of the diagonal terms only after some time, when significant number of modes are excited. Since the mass is kept constant, you can't say at what point in terms of the mass that happens.

    That was also the point of the Don Page's PRL that we cite. He showed that in a thermodynamic system, after some time, all the information in the system is in the subtle correlations between the small subsystems (particles), while particles them selves carry very little or no information. Don Page showed that this is true in the absence of gravity, but it was used as a crucial argument in the firewalls paradox. We showed that this is true in the presence of gravity as well. It is the point that Sabine persistently tries to downplay.

    Best wishes,


  30. Dear Sabine,

    If you can't write a single sentence without twisting the facts, then any further discussion is meaningless. Can I ask you for a big favor? Could you please stop commenting on my papers in future. I do not have time for these public debates.

    Do not get me wrong. I am not angry at you. this is just your style, and I understand it. But I really have more important things to do.

    Best wishes,


  31. @Dejan, Bee

    Why not submit to binding arbitration?

    Luboš is skilled in the art, creative, and not shy about exposing flapdoodle whatever its origination.

  32. "How about a public bet with a realistic but appreciable pay off? EUR 10 thousand?"

    I'm happy to make a sensible bet with anyone on whether there will be micro black holes at the LHC...

  33. "How about a public bet with a realistic but appreciable pay off? EUR 10 thousand?"

    A sensible bet for me would be token tenner (£10 UK Sterling).

    I'm predicting there will be micro black holes at the LHC.

    Any takers?

  34. /* Luboš is .. not shy about exposing flapdoodle whatever its origination */

    :-)) You must be very new at this planet.. :-)

  35. Alice and Bob are entangled.

    Paradoxically for a loss of words (information).

    Schrödinger's cat got their tongues.

    Attempted levity aside, when rating anyone's blog entry just use the learning curve.

    I always learn here.
    That's nothing new here too.

  36. Delete double entry.

    My sincere apologies.

  37. @Dejan,

    I like this -

    "We did not take back-reaction into account..."


  38. Dejan, what you are requesting from Sabine would be a massive disservice to the science community at large.

    Every physics blog and science section of major newspaper has been blaring that your paper solved the black hole information paradox.

    If it wasn't for this blog there'd be no correction to this misrepresentation whatsoever.

    While I appreciate that your paper offers up some interesting physics, your language quite clearly invited this misleading reporting, which in turn amounts to a massive waste of time for everybody who has to figure out that there is far less to it than originally reported.

    And BTW, I fail to see how Sabine quoting your paper verbatim in her previous comment, amounts to twisting your words.

  39. To me, the amazing thing is that anyone still thinks that PRL is a good journal. That may have been the case 30 years ago, but it certainly isn't now: they publish the same sort of junk as anyone else. The main role of PRL nowadays is to get two papers for the price of one.

  40. And one in German...

    Schwarze Löcher: Grüße aus dem Massemonster

    Quite remarkable for a paper that merely reproduced a standard result, no? Surely it's me who is 'twisting the facts' /sarcasm

  41. "A sensible bet for me would be token tenner (£10 UK Sterling).

    I'm predicting there will be micro black holes at the LHC.

    Any takers?"

    I suggested ten thousand, you suggested 10. Who is more confident?

    Nevertheless, I accept. If no-one from the LHC announces such a discovery by the end of 2016, you owe me a tenner. Feel free to suggest the end of another year, but for every year after 2016 the stakes double each year.

  42. "The news even made it to vixra:"

    Damning with faint praise?

  43. It's not this "news", though, just another crackpot paper by a known crackpot claiming to have solved this problem, jumping on the bandwagon, to be sure.

    Read the abstract for a slight chuckle.

  44. As far as I understand, it's impossible to say that Sabine is wrong. you could endorse Einstein results, and in such cases, you could be right.http://www.cscamm.umd.edu/tiglio/GR2012/Syllabus_files/EinsteinSchwarzschild.pdf

  45. This comment has been removed by the author.

  46. "Nevertheless, I accept. If no-one from the LHC announces such a discovery by the end of 2016, you owe me a tenner."

    Alright, Helbig, you're on. If micro black holes are detected this year (and it will be this year) then you owe me a tenner. If not, then I'll pay up. Done.

  47. Science is not people saying you are correct. Gran Sasso superluminal muon neutrinos received an arXiv-load of support. It had to be correct, for so many reasons. Tommy Aquinas.

    Science is the person proving you wrong. Euclid vs. Bolyai; Newton vs. Maxwell, GR, QFT; perhaps another to come. Karl Popper.

    1) Phys. Rev. 104(1) 254 (1956) Crackpots! Physics is mirror-symmetric (Green's theorem).
    2) Phys. Rev. 105(4) 1413 (1957) Two pages. Nobel Prize/Physics same year.
    3) Phys. Rev. 105(4) 1415 (1957) It was a trivial observation...
    4) PNAS 14(7) 544 (1928)...made 28 years earlier, and rejected.

  48. Very interesting and useful article and discussion. Thank you for that. After I read the paper in question, I was looking exactly for discussions like this one.

    It greatly annoys me seeing the media and scientists abuse of headings in scientific articles in order to get public attention and to sell. Or situations when the media and scientists present theories as a fact and forget to clarify that the theories in question have not been experimentally proven (for example String Theory articles in general or the holographic universe theory in particular.) It doesn't serve science, it doesn't serve the truth, people get misinformed and in the end, affects the credibility of science and scientists. The earlier in the process situations like the one explained in this article are exposed, the better.

    See below 2 comments by Dejan Stojkovi, : one in an article for phys,.org and another a posted here as a reply to Sabine Hossenfelder:

    1 - Original phys.org article:

    "According to our work, information isn't lost once it enters a black hole," says Dejan Stojkovic, PhD, associate professor of physics at the University at Buffalo. "It doesn't just disappear."

    2 - Dejan Stojkovic posted comment here:

    "We did not claim that we resolved the full information loss paradox. "

  49. Here is another one that is particularly telling:

    Stunning New Theory: Black Holes Don’t Erase Information

    Where one can read:

    "Further, Stojkovic explain: “an observer standing outside a black hole can recover information about the matter at the heart of the black hole by analyzing particle interactions such as gravitational attraction. Apparently, the scientific community has knows of such correlating information for a while, but this is the first paper flesh out the connection mathematically.”

    Originally, many scientists deemed these correlations as ineffective because they were so minute, but Stojovic calculated that these interactions grow over time, and become large enough to significantly affect calculations.

    “These correlations were often ignored in related calculations since they were thought to be small and not capable of making a significant difference,” Stojkovic said “Our explicit calculations show that though the correlations start off very small, they grow in time and become large enough to change the outcome.”

    This statement is manifestly wrong. They simply do not calculate what an outside observer sees. As Dejan wrote himself above, what they did was to show "that the full density matrix is actually that of a pure state." This is correct, but trivially so, it has been calculated thousands of times (in many textbooks and papers) and it does explicitly *not* explain what the outside observer sees.

    I have a hard time figuring out if he simply doesn't understand the point or if he does and is deliberately lying.

  50. That defines the issue. How could Dejan be confused?

  51. Uhm, after eq 16 one reads: "Since matrices A and B are symmetric and real, the principal axis theorem guarantees that both can be diagonalized simultaneously with respective eigenvalues α and β."

    Those particular two matrices might be commuting for other reasons (although it does not seem obvious at all) but the statement above seems just wrong...

  52. Before some time I pointed here, that if the space-time metric gets inverted at the event horizon, then the definition of entropy must be adjusted accordingly (the expansion is not entropic effect anymore). The question rather is, if the whole problem isn't so poorly conditioned, that the formal models cannot contribute it without resorting to confusing misinterpretations.

  53. Hey Zephir.

    Hvussu sigur ein 'luftpútufarið hjá mær yður í álli' á føroyskum?

    Steðga! Gevst!

  54. Hi Sabine. I think you are fully right on this.
    Carlo Rovelli

  55. /* prove to me why there will not be black holes at the LHC, because I disagree */

    The only "micro-black holes" are produced at LHC routinely already - it's common particles and atom nuclei.

  56. @Dejan,

    You said "Could you please stop commenting on my papers in future. I do not have time for these public debates."

    In a Democracy and in science, people have the right and obligation to give their opinion and to comment. In both cases, it provides a system for checks and balances. It helps unveil the truth and avoid misleading science. I am not a fundamental physics researcher, and I respect too much the discipline to give my opinion about your paper. However just by reading your comments here and by goggling all the comments that you gave in different scientific articles, it is common sense that there is a disparity between what you claim in your paper and the flashy headlines and comments that you give in the scientific articles that make repercussion of your paper.

    Give me a big favor, in the future do not ask anyone, specially a peer scientist like Sabine Hossenfelder, to stop commenting on anything. Your time on the other hand, is as important as everybody else's time.

    Do not get me wrong. I am not angry at you. this is just your style, and I understand it. Thank you very much for your time.

    Best wishes,

  57. Carlo: Thanks.

    Zephir, Darius: Now that you have sorted out your bets, can you please take your discussion about LHC black holes elsewhere, it's really off topic.

  58. Sabine,

    yes, I agree... to continue discussions on micro black holes at the LHC and related matters:


    Best regards,


  59. Dear Sabine,

    I can't believe what I am reading here. Using the cut and past technique and taking the sentences out of context you can prove whatever you want. I could understand if some of your readers use this technique, buy Sabine, you are a member of scientific community, you should know better.

    For the record, the information loss paradox is very complex. We never claimed anywhere that we resolved the full information loss paradox. There is an issue of what an asymptotic observer who never witnesses the formation of the horizon and singularity during the collapse observes, but there is also an issue of what happens to that information from an infalling observer's point of view: is this information bleached, doubled or transferred non-locally. There are also the issues of firewalls etc. But I stand behind the title of our paper "Radiation from a collapsing object is manifestly unitary", which is an important part of the puzzle. It tells you about the one of the possible ways to encode information in radiation produced by a collapsing object.

    Moreover, even if it happens that I was wrong, and that we did not show that an outside observer sees unitary evolution, results contained in the paper are very general, and make an important step toward the resolution. If you are unable to see that, then this is your problem, and you can disagree with me.

    However, the most important issue here is your hostility and rudeness you expressed toward many authors, journal editors and referees. If you think that I am the only one who thinks so, you are very wrong. This is the reason I would like to respectfully you ask you one more time, to stop using my name in your blog. Starting now.

    Best wishes,


  60. "My love she speaks like silence, without ideals or violence
    She doesn't have to say she's faithful
    yet she's true like ice, like fire
    People cary roses make promises by the hour
    My love she laughs like flowers
    Valentines can't buy her" ...

    "The cloak and dagger dangles
    Madams light the candles
    In ceremonies of the horsemen
    Even the pawn must hold a grudge
    Statues made of match sticks
    Crumble into one another
    My love winks, she does not bother
    She knows too much to argue or to judge."

    Bob Dylan Love Minus Zero, No Limit

  61. Dear Dejan,

    I don't usually comment on blogs but your belligerent attitude has forced me to this time. I have some background in physics and what Sabine wrote is exactly right. Deriving the form of the Hawking radiation is a rather standard problem covered in any graduate level GR/Cosmology course. Also it is discussed in great detail in most GR textbooks like that of Carroll or Wald. There is no controversy that the pair production process is unitary. However, the infalling particle doesn't reach an asymptotic observer. So to describe what he sees, you have to trace over the infalling radiation - obtaining a thermal density matrix. We don't know what's the ultimate fate of the infalling particle and according to GR, the outside observer only has access to the thermal Hawking radiation. This, in a nutshell, is the black hole information problem.

    In your paper you derive that pair production is unitary by a novel method. While this has pedagogical value the result itself is hardly new. When you trace over the infalling part, you again get back a thermal density matrix. This is nothing to tom-tom about. In fact, I'm worried about the quality of PRL now that it has started to publish papers like this.

    However, as Sabine pointed out your paper has been misinterpreted and getting a lot of traction in the media. Instead of acknowledging this, you try to browbeat Sabine saying that she should not criticize your papers any more. This kind of behaviour does not behoove a scientist.

    Moreover, in your last post you try to intimidate Sabine by saying, "the most important issue here is your hostility and rudeness you expressed toward many authors, journal editors and referees. If you think that I am the only one who thinks so, you are very wrong." Argument from authority, really?

    I hope you learn your lesson from this episode and modify your behaviour accordingly.


  62. Sudip: you mean befit, not behoove. Used to be, being proper was considered necessary. So "It doesn't behoove you" means "you aren't required to".

    Dejan: The source of these direct quotes attributed to you by the media is the UB press release. It quotes you saying "This is an important discovery". And the words "black hole" came out of your explanation why it's important. There's an expression for someone who tells us you're not claiming anything extraordinary in your paper, but makes those same extraordinary claims to the public: two-faced. You got caught with your hand in the cookie jar, and then call mommy a name for coming home early.

  63. Wikitionary says the #1 meaning of behoove is 'to suit, to befit': http://en.wiktionary.org/wiki/behoove. Also was that the only thing you found worth commenting?

  64. As I tried to indicate in my comment above the point is not purity as such but when purity is restored for the external observer if we assume that the black hole evaporates completely via Hawking radiation i.e. if purity is assumed.

    I gave a quick look at the referenced material since this is the best way to understand the intentions of the authors when they wrote their paper.

    Specifically in page 14 of the Mathur’s paper it is written.

    “It is logical to ask if such small corrections can perhaps invalidate Hawking’s argument, and remove all entanglement between the quanta bi and the (M, ci) quanta in the hole. If this happens, there would be no paradox, since the hole containing (M, c) can vanish, and we will be left with a pure state of the bi quanta, presumably carrying all the information of the initial matter |ψ> M.

    It is a very important fact that such small corrections do not change the conclusion reached in the Hawking argument. We will call this fact the ‘stability of entanglement of the Hawking state.”

    The key phrase is:

    “there would be no paradox, since the hole containing (M, c) can vanish, and we will be left with a pure state of the bi quanta”

    So basically this is what they are trying to do here i.e. to study the nature and strength of such corrections and how fast they can restore purity and that’s why they don’t feel the need to trace out anything; they assume that everything inside the BH will reach eventually the external observer.

    This means that purity is a prerequisite of their calculation and implicitly is taken as an assumption.

    In fact Hawking argument has two parts. The first is the usual one that due to the horizon the information cannot reach the external observer and the second part is that even if we assume purity i.e. that the BH evaporates completely and the whole information reaches the external observer via Hawking radiation this happens very late of the evaporation process when the BH reaches the Planck scale limit which as we know is too late.

    But Hawking reached that conclusion using only leading order approximation (since the assumption is that the corrections are too small to change anything) and the authors are trying to include the corrections too. Presumably they have found that the corrections could be strong enough(I have no comment on this).

    So the authors address the second part of Hawking argument with purity as an assumption and not the first part.

    In that sense their paper has a true value but unfortunately they have chosen a very bad title that caused all these misunderstandings.

    The title wrongly indicates that they are trying to deal with the first part of Hawking's argument when in fact they are dealing with the second part.

    Anyway this is how I understood things.

  65. Many decades ago, the then editor of PRL (maybe Sam Trieman) noted that everybody agreed that half the papers in PRL were trash. The problem was that they didn't agree on which half.

    Maybe the standards haven't really changed all that much.

  66. Giotis,

    That is what I thought too, at first. But see that Dejan here in the comments and also in the paper points out repeatedly and explicitly that the new finding is supposedly that the full radiation matrix is unitary, which is clearly not new. Yeah, maybe one could use this approach for the purpose you point out, the problem with this is that I don't know how to interpret these coefficients. Best,


  67. Sudip, Mike:

    Thanks for your support. I find the exchange with the author extremely depressing.

    See the bigger problem with this? I question the novelty value of some published research (and notice that I didn't even say the paper is wrong) and in return I am marked 'rude' and 'hostile'. Behavior like this greatly discourages criticism within the community. On the other hand, we are supposed to think that it is totally appropriate to oversell research results to the press. Both trends are highly problematic because they benefit the growth of unpromising research directions.

    (And, sure, the PR person played a role in this too.)

    Just for the record, Carlo (in the comments above) took my occasional criticism quite gracefully, as I'd expect from a scientist (even though I was much harsher on him than on Dejan). I simply think criticism is part of normal scientific debate.



  68. Mister D last comment (12:49 PM, April 10, 2015) sounds to me like a polite but unacceptable intimidation. The request is even more unacceptable because it comes from a member of the scientific community.

    Regardless of whether mister D work is right or wrong, I believe mister D's request of not mentioning his name in the post or the request of not discussing his work goes against the right of freedom of speech. Personally I do not have anything against mister D and I will be happier than mister D if his work helps resolve the information paradox (that has been around for almost 40 years and involved the work of many brilliant minds.) However, I am convinced that any member of the scientific community must be able to make comments on any other member's work without being pressured to stop. That makes a healthy system of check and balances, helps the advancement of science and the generation of new ideas. We have too many examples in the history of science of what happens when scientists are forced to stop criticizing and expressing his ideas.

    And no matter how much I love myths, I do not want to live in the Middle Ages or worst, I do not want to live in a totalitarian regime.

    I want science to rock.

    Thank you Sabine for your time and post. We do not have too many women in science and that makes you more valuable. Wish you the best in your career.


  69. Sabine is making a very good work with her blog. People must know it!

  70. Uncle AI.
    Your funniest remark yet has disappeared. I know not whether you or Bee deleted it but your suggestion was an excellent experiment regarding theoretical physicists.
    Although I believe I can show the fundamental result that he would find two s-it for brains both wrong. Bee would acknowledge this but correctly point out that this result is well established and says nothing regarding what would happen if they were not spatially separate but in one room. In that we can never achieve this Woit declare that it is not even wrong to think about such things. My theory is that some people are so intelligent that they approach being smart but that it is always a mixed state. Here Dejan should admit he is wrong because he is.

  71. I haven't deleted any of Uncle's comments, and there's nothing in the spam queue either. I deleted on of Darius' comments.

  72. CIP, Regarding PRL standards. I recently was asked for opinion on a paper considered for PRL in an odd arrangement, in which I wasn't really asked to review it, but merely whether it was indeed relevant for 'my community' (in this case, black holes) as the authors claimed. The honest answer to this was no, and I am afraid that was sufficient reason to reject the paper (which was otherwise totally fine and also interesting). So I do think they really did try to change things, but I whether that was a change for the better or not is left for the asymptotic observer to judge...

    (Incidentally, the move of PRL to allow editors to reject papers without sending them to review at all pissed of a lot of my colleagues. I can understand the "Who ft do they think they are" sentiment, but on the other hand I did have the hope that in the end we'd benefit from it. Now that some time has passed, it doesn't seem like it worked.)

  73. @Bar,

    Bee is most forgiving of any skepticism I may express toward a science that no longer produces empirically falsifiable outputs. Three conditions:

    1) An idea longer than ~100 words is not there.
    2) (1) without empirical test is not there.
    3) Citations. Whether standing on giants' shoulders or corpses' bellies, show you know the territory.
    4) Know when to stop.


    "If we add a single atom to black hole, then the black hole will become heavier by just a single atom." Smartless. Binding energy is negative. A bound system must mass less than its separated constituents. Calculate, don't guess.


  74. Uncle AI and Bee, the comment is still there. Presumably my aging eyes.

  75. Can't believe what I am reading here either. The attitude on display by Dejan Stojkovic is nothing but despicable.

    Sudip put it best.

    The only thing to add is that Mr D. better get used to getting much more scrutiny from blogs.

  76. Very interesting that after Sabine wrote her blogpost on April 7, the authors hurriedly added the following sentences in the conclusion of version 3 on April 8: "For unitarity to be manifest to an observer, he has to be able to observe the total density matrix, i.e. all the created modes and correlations between them. If some of the modes are lost into the singularity, then the incomplete density matrix may not look like that of the pure state. However, there are strong indications that quantum effects should be able to rid gravity of singularities, just as it was the case with the singular Coulomb potential (see for example [23])." If these (honest) statements were present in the original version, nobody would have cared about this paper and it would never have been accepted at PRL.

  77. Does anybody worry about information loss over the other horizon? Thanks to dark energy everything beyond redshift z=1.8 is already forever out of causal contact with us, and distance is creeping ever closer.

  78. Sabine,

    I don't understand why my comment was removed.

    Recently I went to a theory department open day, where I stated there was a connection between Hawking radiation and dark energy. "Hawking radiation is dark energy," I finally said. A prominent academic replied to my face, "No.", without further explanation or allowing me to elaborate.

    Surely this is not how science should progress.

    Best regards,


  79. CIP: Off-topic.

    Darius: You have posted a lot of comments in this thread, and they don't contain a lot of interesting information, that's why. You are simply limiting the readability of everybody else's comments. It's taken years until Zephir learned that my biggest problem with his comments isn't the content but the frequency. I hope you're somewhat quicker on your feet and learn to keep your comments short and to the point, so I don't have to scrape them out.



  80. Sabine,

    That's understandable, my post certainly did not contain that much scientific information, however, it did not contain a potentially informative gedanken experiment:

    What if we posit the observer of information inside the black hole?

    In any case, I will leave it at that: short and to the point.

    Best regards,


  81. Sabine, I hope you keep commenting on papers like this one no matter what the authors have to say about it. While I'm sure professional physicists working on black hole information can assess the merits of the paper for themselves, there is a larger group of people out there - like me - who studied physics in school but then scattered into other professions. Nevertheless, I know enough to understand a statement like "The authors in the paper never trace out the part behind the horizon, so it’s not surprising they get a pure state." That right there tells me enough to dismiss the more grandiose claims being made about this paper in the popular press.

    Sudip, I appreciated your comment emphasizing this point as well.

  82. Sudip: Yes, I upvoted your post, as I agreed with all your points. I mainly wanted to add, it's clear DS did what he denies. His problem isn't that the accusation is unjust. It's rather that the truth hurts.

    As for behoove, I suggest not relying on any one def in any one source. But let's start with:
    The original root meant "to need". It supports my claim, but is not definitive. There are people who use behoove as you did so you are not alone, and may be correct. I ask you to look at examples. I believe you will find "it behooves us" can usually be changed to "we need to" WLOM (meaning). One source (Roget) says the "beseem" sense is archaic: beseem and befit are very close. In short, take my opinion with a grain of salt, but this writer maintains, befit was appropriate. You don't need to agree. And avoid "does not behoove": it may or may not be ambiguous; it's confusing.

  83. Actually, what SH could have done was to politely invite Prof Stojkovic to write a guest post here, and then you could have a civilized debate. Instead that has happened at, of all places, Lubos Motl's blog!

    One thing prof S said is definitely correct: a *lot* of people really hate this style of blogging. You may not *care*, but make sure you *know*.

  84. Rastus,

    Dejan had all chance to explain himself in the comments. Instead he chose to attack me personally. He had all chance to ask for a guest post. He didn't. He even had a chance prior to publishing by email to explain himself - and let me add that this exchange did cause me to considerably take off the edge of this blogpost which in my book is pretty nice, it only got nasty in the comments. A guest post at Lubos' will certainly go a long way to restore his credibility. Best,


  85. "Does anybody worry about information loss over the other horizon? Thanks to dark energy everything beyond redshift z=1.8 is already forever out of causal contact with us, and distance is creeping ever closer."

    Be careful about arguing too far from analogies between black-hole horizons and cosmological horizons. For starters, the latter are relative: what is on the horizon to one person is well within it for another. Second, nothing strange happens there (by the same argument).

  86. Recently I went to a theory department open day, where I stated there was a connection between Hawking radiation and dark energy.

    On what grounds? Where is your evidence? Can you explain why the derivation for Hawking radiation is the same even in a universe without dark energy?

    "Hawking radiation is dark energy," I finally said. A prominent academic replied to my face, "No.", without further explanation or allowing me to elaborate.

    What should he have done? Said "OK, if you want"? If one allows any and everyone to elaborate their pet theories at such open days, it will be dominated by crackpots. One has to draw the line somewhere. A statement which, to any physicist, is obvious bunk should produce such a reaction.

    Surely this is not how science should progress.

    What do you suggest? Should we take your word for it?

    Publish a paper, or at least write something on your blog, which supports your idea.

  87. Darius,

    Hawking radiation, as the name says, is radiation. Dark energy doesn't have the same equation of state as radiation. Consequently, hawking radiation can't be dark energy. You merely demonstrate that you don't know what you are talking about. I will delete further off-topic comments like this (Phillip!). Thanks,


  88. Interesting controversy ! I do not know enough about the subject to make any scientific comment. But I would say that in general controversies are healthy for science. There could be sacrificial lambs in the process! But in the long run this is good for science. Let the best theory win! Because of the "40 years controversy" I would like to see comments of people who have actually published refereed papers on the information paradox. Is it possible to ask them to express their opinion?
    Some people, who do not agree with the conclusions of the paper, blame PRL for quality going down. This is not fair. It just means that it went to a referee who thought this was a valuable contribution which deserved urgent publication.

  89. It is interesting that nobody here notices the statements from the original article

    "The research marks a significant step toward solving the information loss paradox."

    "Stojkovic and Saini’s new paper helps to clarify the story."

    In the original article you can't find the statement that we solved the information loss paradox.

    Indeed, I noticed many spin-off web pages with titles like "Hawking was wrong, black holes do not destroy matter", but I have nothing to do with these statements.

    Anyway, after the storm has passed, I can say that I feel at least partially responsible for this mess. This is not what I wanted and it does not make me happy. It certainly got blown out of proportions.



  90. Hi Dejan,

    Thanks for the follow-up comment, much appreciated! Best,


  91. Dear Sabine,

    You are very welcome!

    Best wishes,



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