Thursday, April 06, 2017

Dear Dr. B: Why do physicists worry so much about the black hole information paradox?

    “Dear Dr. B,

    Why do physicists worry so much about the black hole information paradox, since it looks like there are several, more mundane processes that are also not reversible? One obvious example is the increase of the entropy in an isolated system and another one is performing a measurement according to quantum mechanics.

    Regards, Petteri”

Dear Petteri,

This is a very good question. Confusion orbits the information paradox like accretion disks orbit supermassive black holes. A few weeks ago, I figured even my husband doesn’t really know what the problem is, and he doesn’t only have a PhD in physics, he has also endured me rambling about the topic for more than 15 years!

So, I’m happy to elaborate on why theorists worry so much about black hole information. There are two aspects to this worry: one scientific and one sociological. Let me start with the scientific aspect. I’ll comment on the sociology below.

In classical general relativity, black holes aren’t much trouble. Yes, they contain a singularity where curvature becomes infinitely large – and that’s deemed unphysical – but the singularity is hidden behind the horizon and does no harm.

As Stephen Hawking pointed out, however, if you take into account that the universe – even vacuum – is filled with quantum fields of matter, you can calculate that black holes emit particles, now called “Hawking radiation.” This combination of unquantized gravity with quantum fields of matter is known as “semi-classical” gravity, and it should be a good approximation as long as quantum effects of gravity can be neglected, which means as long as you’re not close by the singularity.

Illustration of black hole with jet and accretion disk.
Image credits: NASA.

Hawking radiation consists of pairs of entangled particles. Of each pair, one particle falls into the black hole while the other one escapes. This leads to a net loss of mass of the black hole, ie the black hole shrinks. It loses mass until entirely evaporated and all that’s left are the particles of the Hawking radiation which escaped.

Problem is, the surviving particles don’t contain any information about what formed the black hole. And not only that, information of the particles’ partners that went into the black hole is also lost. If you investigate the end-products of black hole evaporation, you therefore can’t tell what the initial state was; the only quantities you can extract are the total mass, charge, and angular momentum- the three “hairs” of black holes (plus one qubit). Black hole evaporation is therefore irreversible.

Irreversible processes however don’t exist in quantum field theory. In technical jargon, black holes can turn pure states into mixed states, something that shouldn’t ever happen. Black hole evaporation thus gives rise to an internal contradiction, or “inconsistency”: You combine quantum field theory with general relativity, but the result isn’t compatible with quantum field theory.

To address your questions: Entropy increase usually does not imply a fundamental irreversibility, but merely a practical one. Entropy increases because the probability to observe the reverse process is small. But fundamentally, any process is reversible: Unbreaking eggs, unmixing dough, unburning books – mathematically, all of this can be described just fine. We merely never see this happening because such processes would require exquisitely finetuned initial conditions. A large entropy increase makes a process irreversible in practice, but not irreversible in principle.

That is true for all processes except black hole evaporation. No amount of finetuning will bring back the information that was lost in a black hole. It’s the only known case of a fundamental irreversibility. We know it’s wrong, but we don’t know exactly what’s wrong. That’s why we worry about it.

The irreversibility in quantum mechanics, which you are referring to, comes from the measurement process, but black hole evaporation is irreversible already before a measurement was made. You could argue then, why should it bother us if everything we can possibly observe requires a measurement anyway? Indeed, that’s an argument which can and has been made. But in and by itself it doesn’t remove the inconsistency. You still have to demonstrate just how to reconcile the two mathematical frameworks.

This problem has attracted so much attention because the mathematics is so clear-cut and the implications are so deep. Hawking evaporation relies on the quantum properties of matter fields, but it does not take into account the quantum properties of space and time. It is hence widely believed that quantizing space-time is necessary to remove the inconsistency. Figuring out just what it would take to prevent information loss would teach us something about the still unknown theory of quantum gravity. Black hole information loss, therefore, is a lovely logical puzzle with large potential pay-off – that’s what makes it so addictive.

Now some words on the sociology. It will not have escaped your attention that the problem isn’t exactly new. Indeed, its origin predates my birth. Thousands of papers have been written about it during my lifetime, and hundreds of solutions have been proposed, but theorists just can’t agree on one. The reason is that they don’t have to: For the black holes which we observe (eg at the center of our galaxy), the temperature of the Hawking radiation is so tiny there’s no chance of measuring any of the emitted particles. And so, black hole evaporation is the perfect playground for mathematical speculation.

[Lots of Papers. Img: 123RF]
There is an obvious solution to the black hole information loss problem which was pointed out already in early days. The reason that black holes destroy information is that whatever falls through the horizon ends up in the singularity where it is ultimately destroyed. The singularity, however, is believed to be a mathematical artifact that should no longer be present in a theory of quantum gravity. Remove the singularity and you remove the problem.

Indeed, Hawking’s calculation breaks down when the black hole has lost almost all of its mass and has become so small that quantum gravity is important. This would mean the information would just come out in the very late, quantum gravitational, phase and no contradiction ever occurs.

This obvious solution, however, is also inconvenient because it means that nothing can be calculated if one doesn’t know what happens nearby the singularity and in strong curvature regimes which would require quantum gravity. It is, therefore, not a fruitful idea. Not many papers can be written about it and not many have been written about it. It’s much more fruitful to assume that something else must go wrong with Hawking’s calculation.

Sadly, if you dig into the literature and try to find out on which grounds the idea that information comes out in the strong curvature phase was discarded, you’ll find it’s mostly sociology and not scientific reasoning.

If the information is kept by the black hole until late, this means that small black holes must be able to keep many different combinations of information inside. There are a few papers which have claimed that these black holes then must emit their information slowly, which means small black holes would behave like a technically infinite number of particles. In this case, so the claim, they should be produced in infinite amounts even in weak background fields (say, nearby Earth), which is clearly incompatible with observation.

Unfortunately, these arguments are based on an unwarranted assumption, namely that the interior of small black holes has a small volume. In GR, however, there isn’t any obvious relation between surface area and volume because space can be curved. The assumption that such small black holes, for which quantum gravity is strong, can be effectively described as particles is equally shaky. (For details and references, please see this paper I wrote with Lee some years ago.)

What happened, to make a long story short, is that Lenny Susskind wrote a dismissive paper about the idea that information is kept in black holes until late. This dismissal gave everybody else the opportunity to claim that the obvious solution doesn’t work and to henceforth produce endless amounts of papers on other speculations.

Excuse the cynicism, but that’s my take on the situation. I’ll even admit having contributed to the paper pile because that’s how academia works. I too have to make a living somehow.

So that’s the other reason why physicists worry so much about the black hole information loss problem: Because it’s speculation unconstrained by data, it’s easy to write papers about it, and there are so many people working on it that citations aren’t hard to come by either.

Thanks for an interesting question, and sorry for the overly honest answer.


  1. bee:
    "So that’s the other reason why physicists worry so much about the black hole information loss problem: Because it’s speculation unconstrained by data, it’s easy to write papers about it." you seem to be getting more disenchanted (and cynical) about your chosen field of research recently. this is unfortunate for you but to the great benefit for your readers who are bombarded non-stop by theoretical physicists who promote their ideas and themselves (no need to mention their names; we all know who they are). perhaps it's time to stop to referring their work as speculation and refer to it as "mathematical masturbation" "as Richard Feynman declared "Physics is to mathematics like sex is to masturbation." this is not meant to criticize masturbation which as Woody Allen said "'Don't knock masturbation. It's sex with someone you love.". i hope you don't, as a result of your disillusionment, leave physics. your in-depth analysis of papers (not to mention your music videos) which is unique amongst physics blogs, would be greatly missed. there are other field of theoretical physics, more closely connected to, and driven by, experiment, that could use the sort of analysis and insight you bring to your blog.

    best regards,


  2. Fantastic discussion. Eminently readable by an amateur like me!

  3. I would suggest the following approach (slightly inspired from my background in Computer Science and Algorithms ;-)

    First, find as many points as possible that are in conflict of the information loss problem and that would need to be scrapped to explain it. For example "maybe information is not lost but kept somewhere". "maybe hawking radiation does not really exist", etc. Branch out as detailed as possible and as "deeply" as needed with as many single "points" you can make out.

    Then, for each point that you found, try to find the implications that scrapping this particular point brings. My guess is that in most cases this would cascade and you'd end up needing to scrap very large parts of physics. then try to find the points with a "minimal" cascading effect and work from that point to try and find replacements/alternative theories for all that has been scrapped.

    I know, the idea is probably quite naive (especially coming from me, since I don't have a strong quantum mechanical background) but I get the feeling that such a "meta-discussion" has not yet been produced.


  4. Michael,

    Yes... Indeed that is pretty much the gist of the argument Lee and I led in the above mentioned paper. Do you think there's a way to make this more formal? Maybe with some kind of Bayesian analysis? I'd be very interested to learn if that's possible.

  5. Hi! I've always had trouble understanding how Hawking Radiation can result in a decrease in the mass of the black hole..

    The way I picture it is that a pair of particles pops into existence at the boundary of the event horizon and one falls in while the other escapes. But both the particles have the exact same amount of mass, don't they? How does that result in a mass decrease?

  6. dr.dna

    Because the total energy for the pair has to come from somewhere and it has to be taken from the background field. But really that doesn't even matter: The total energy is conserved, which means if something escapes to the far distance then the mass/energy of what's left behind must decrease.

  7. Susskind's ‘Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics’ was a good reading though.

  8. A quote and 2 questions.

    Regarding the widespread picture of virtual pair creation with one falling in, Daniel Harlow writes:

    Although I won’t use it in what follows, there is a heuristic explanation of Hawking radiation that is occasionally brought up. The idea is that entangled pairs of particles are constantly jumping into existence near the horizon via vacuum fluctuations, and sometimes one of them falls in and one of them gets out. This cartoon has several problems if it is taken literally, among them that the “particles” involved have wave- lengths comparable to the size of the black hole and that the Hawking process isn’t really stochastic, and in my view it tends to create more confusion than it resolves.

    I have read similar claims that the picture is just inaccurate. Certainly, the picture of virtual particle pairs "jumping into existence" makes no sense. Do you agree?

    The second question is with respect to using global energy conservation (note: not local!) to argue for the mass decease of the black hole. That's just what Hawking does in his first paper. But is we grant that conservation laws arise from symmetries via Noether's theorem, then we only expect global energy conservation where there is a global Killing field. And if the black hole evaporates there is no global Killing field. So how is the appeal to global conservation justified?

  9. Tim,

    Yes, I agree with Daniel. As I explained here: Hawking radiation is not produced at the horizon.

    Energy and mass can be globally defined in certain circumstances and black hole collapse (in asymptotically flat space) is one of them (the probably most studied case). The first some paragraphs of this paper may shed some light on the situation.

  10. ""The temperature of the Hawking radiation of black holes that we observe is so tiny there’s no chance of measuring it.""

    Hello Bee,
    what do we observe while beeing too tiny to be measured?
    I guess a "which" instead of "that" might heal the sentence.

  11. George,

    Ah, I see the problem. I've fixed this sentence (or so I hope). Thanks for pointing out!


  12. Sabine,

    I understand that it is sometimes easier to get across a hard idea with a simplified but inaccurate first pass. It looks to me as if that is what is happening here, so let me press a little further.

    As I understand it, the principle of global conservation being appealed to here is the conservation of the quantity that has been termed "ADM mass" in asymptotically flat space-times. So it is not the conservation of "energy" that arises via Noether's theorem in a space-time with a global Killing field. The "ADM mass" is not a local quantity that is summed over to get a global value.But that seems to be exactly the assumption lying behind this sentence of yours:

    The total energy is conserved, which means if something escapes to the far distance then the mass/energy of what's left behind must decrease.

    If by "total energy is conserved" you are referring here to the ADM-mass, then the local talk ('what's left behind") makes no obvious sense. And the association of the ADM mass with anything called "energy" is not transparent.

    If you can shed some light, that would be greatly appreciated. Or at least confirm that the global conservation principle being appealed to is the quantity called ADM mass.



  13. @Sabine

    Shouldn't the vacuum energy density as measured in cosmology (the cosmological constant) constrain the amount of Hawking Radiation emitted?

  14. Tim,

    The level of detail in my reply aimed to match my guess at the level of expertise of the person asking the question. So let me say this: Stress-energy is of course still locally conserved, so clearly you can't make particle pairs out of nothing if they both have positive energy. In Hawking's calculation actually one of the particles has negative energy. That's because the calculation assumes the background is fixed, hence there's no way to produce particles from it. Just how to include the change of the background in response to the pair production is the infamous 'backreaction' problem (which this blog is named after) and for all I know it's still unsolved. So, actually nobody knows just exactly "where" the energy of the particle pair comes from, except that because of local energy conservation it has to come from somewhere.

    Having said that, the other part of my statement refers to the ADM mass. I think in this case it's easier to understand: If something gets away to infinity, whatever remains behind must have less mass. I'm not sure what you mean there with your question. Do you mean the particle doesn't have mass or energy at infinity? The mass 'left behind' is the parameter 'M' in the Schwarzschild solution (or Vaidya if you want to include a flux). I wouldn't call that a 'local' quantity (you get it from an integral condition) but assuming spherical symmetry for all I know it's well-defined. Hawking's original attempt to include backreaction was to simply subtract the energy of the emitted radiation from this 'M' of what's left behind. (And ever since we've discussed if that's a good approximation.)



  15. Stuart,

    Well, yes, the amount of energy density emitted by Hawking radiation shouldn't exceed any constraints on local energy densities near black holes, but the energy-density of Hawking radiation (as its temperature) is negligibly small for black holes in the mass ranges we observe. (And it does not behave like dark energy as your question seems to assume.)

  16. "The reason that black holes destroy information is that whatever falls through the horizon ends up in the singularity where it is ultimately destroyed."

    It seems to me that until we have a consistent theory of quantum gravity, the destruction of matter and radiation by the singularity cannot be assumed. Consequently, information destruction by the singularity cannot be assumed, either.

    Thank you for another great post!

  17. The discussion of Baysian analysis etc brings up an interesting point: can artificial intelligence or machine learning actually have an impact on theoretical physics? That is, if you can feed all of the papers on the information paradox into a machine learning system, can it point out where the most fruitful directions for future research lie, in an unbiased manner?

  18. "you’ll find it’s mostly sociology and not scientific reasoning" is understandable but problematic. Many will say that sociology IS a hard and quantifiable science, but there is little agreement on how to proceed. Because peple generally do not understand what information is, this leads to miunderstandings like "Information loss/diappearance = information non-existence.

  19. "they contain a singularity " Two singularities’ merger violently shuffles orbital angular momenta. " the singularity is hidden behind the horizon and does no harm" A primordial rather than accretive Kerr black hole's majority mass is its "hidden" central singularity. Source its enormous spin angular momentum.

    LIGO GW150914[1] observed 35 + 30 solar mass BHs inspiral, merge, emit 4.6% binding energy, then 0.05 second ringdown[2] - two soap bubbles touching then popping into one. LIGO GW151226[3], 14.2 and 7.5 solar masses, 4.6% binding energy, 0.005 second ringdown[4]. All BH observables occupy a 2D+ε shell absent “interior” contents.

    " the universe – even vacuum – is filled with quantum fields of matter" Enantiomorphic structural chemistry tests microscopic vacuum achiral isotropy toward hadronic matter seven different ways. One day in a pulsed-chirp FT µwave spectrometer (3:1 enantiomers’ cryogenic rotational spectra) heals baryogenesis, dark matter...SUSY, M-theory, or not. Look.

    "Hawking radiation" Cosmic microwave background is 2.72548 kelvin black body emission. Thermal equilibrium BH: 0.00754 Earth masses, 0.006689 cm radius , l2.43×10^35 gigayears lifetime[5]. No BH net evaporates.

    Physical theory has deep holes containing horizontal but not vertical exits - wander not climb. "8^>)


  20. Bill,

    Well, yeah, that's what I go on to explain is the "obvious solution" that has been discarded on spurious grounds.

  21. Hi,

    I don't quite understand how you are able to say that every process is reversible in principle. If I have an integrated circuit that adds two bytes of numbers X and Y and produces the resulting number as a byte Z, then clearly once I have added 3+4 to get 7, I can't possibly reverse this process in time to get 3 and 4 back in the input. Or have I misunderstood what you mean by reversible?


  22. I have a guess. But it depends on the answer to my last question. So I repeat my last question.

  23. What does the fact that we have not seen small black holes at LHC mean? Does it mean that small high energy black holes evaporate very fast before you can see them? This may give some support to the idea of Hawking radiation. On the other hand it may also mean that the idea that BH must be formed when you dump lot of energy in a small volume may be wrong!

  24. I would say your post was more helpful than all of Susskind’s “Black Hole Wars”.

    The definition of “information” is thrown out as an assumed bit (bad pun intended) of knowledge. Something is wrong with the undergraduate education program. I can’t find “information” in the index of Dirac’s “The Principles of QM”, Shankar’s “Principles of QM”, Feynman’s Lectures Volume III, Mandl and Shaw’s “Quantum Field Theory.” I do find lots of words in books about Shannon and his measure of information in books about Claude Shannon.

    It would be really nice to see definitions and EQUATIONS using those definitions if losing said quantity is going to make the world unsafe for quantum mechanics.

    OK. It’s all just over my head.

  25. Ambi Valent,

    Sorry I can't make sense of your comment. Are you sure it belongs in this thread?

  26. Naren,

    There are many theories which you can invent that have processes which are not reversible. The one you seem to have in mind is one. However, the fundamental laws of nature that have been probed to very high precision are reversible. Fundamentally, hence, everything is reversible. (Except for black hole evaporation.)

  27. John,

    No, there is no definition of 'information' involved here. The problem is entirely independent on exactly what is meant by information. The contradiction comes about because the process is irreversible. The name 'information loss problem' is therefore quite misleading. Indeed your complaint along the lines 'well we don't know what information is etc' is the most common comment I get about this. So please note: It's irrelevant. You don't need a definition of information to see that there is a problem.

  28. kashyap,

    it means there are no large extra dimensions.

  29. I agree that casting this in terms of information is not helpful, but it can be defended in this way: in a bi-deterministic theory that is deterministic in both time directions) the state on a Cauchy slice fixes the state on the entire space-time, so each Cauchy slice contains "complete information" about what happens everywhere and at all times. The standard evolution equations for quantum theory (Schrödinger, Dirac) are bideterministic. So if you have no collapses, and there is nothing but the quantum state, in this sense information is preserved from the state on any Cauchy slice to the state on any other. Every physical fact deducible from the state on one slice is deductible from the state on the other.

    The issue is essentially determinism, not Shannon information. It is kind of ironic that quantum theory, which was long touted as fundamentally indeterministic, is now regarded as a paradigm of determinism.

  30. Tim,

    Well, yes, that's a way to put it, but you didn't define what information is either. Not so surprisingly, because as I said above it's not necessary. What you call 'bi-determinism' is the same as reversibility.

  31. Hi Sabine,

    I wasn't trying to define information, just posting a guess about how the talk of information preservation got started.

    It's a tiny nit, but bi-determinism is not logically the same as reversibility. For example, think of a Hoyle steady state theory, but where the place and time that new particles are created is fixed by a strict rule rather than random. Then I can both predict and retrodict, but the expansion is physically irreversible.



  32. Tim,

    Yes, that's probably the reason why it's called information loss.

    Ok, I think we've strayed somewhat from the topic there, but why is the example you name 'physically irreversible'? (I'm not even sure what you mean by that. What's the difference between 'irreversible' and 'physically irreversible'?)

  33. Thank you for writing this. Over the years I learned a lot from the 'Dear Dr. B.' series. This time however I got stuck on the following paragraph:

    'Hawking radiation consists of pairs of entangled particles. Of each pair, one particle falls into the black hole while the other one escapes. This leads to a net loss of mass of the black hole, ie the black hole shrinks. It loses mass until entirely evaporated and all that’s left are the particles of the Hawking radiation which escaped.'

    This seems strange: how can the black whole disappear if it keeps one in every two particles it once had? It seems to me that the shrinking process stops when it has half of its original mass. Also, it seems to that from the black hole's perspective it is the particles that fell in rather than the particles that escaped that make up 'all that is left'.

    Clearly I am misinterpreting the paragraph, but would you be so kind to clear up my misconception?



  34. Vincent,

    Sorry about that. The total energy is conserved, so if particles escape this means the remaining mass of the black hole has to shrink. Roughly speaking, imagine the energy of the pair being taken from the background field. For more details, please read the comments above where I discussed this already with someone else.

  35. Sabine,

    You mention in your explanation that quantum measurement is fundamentally different from the Black Hole information loss paradox. I'm not sure this is the case. You tacitly assume something special happens during a quantum measurement that is irreversible. What is that something? It's been a long time since I've done any work in this area, but I recall studying many attempts to explain it within the context of standard quantum mechanics. In each of those cases a quantum measurement is very analogous to the irreversibility you see in thermodynamics. So it seems to me that quantum measurement is actually reversible but in practice impossible or something fundamentally irreversible happens.


  36. Sabine,

    The obvious physical example to discuss is a process that violates CP, like kaon decay. At least prima facie, since it violates T is it irreversible. But there are controversial issues there that, as you say, are off topic.

  37. Tim,

    A process doesn't have to be symmetric under time-reversal to be reversible, these are two separate things. Also, I don't see what CP violation has to do with your Hoyle example? In any case, if you think there's a difference between reversibility and what you call bi-determinism I'd like to know what you mean because I don't understand that. Feel free to send me an email, it's hossi[at]

  38. Dr. Bee,

    I’m a lay reader and very naive on how virtual particles work. My understanding is that they always come in pairs of equal absolute energy (one negative/one positive) to obey energy conservation laws.

    When virtual particles form near the event horizon, one may fall in towards the BH while the other may leave away from the BH.

    Sometimes the negative energy particle will fall inside the BH with he positive energy particle would stream away from the BH, thus causing the BH to loss mass and the rest of the universe the gain the same amount of mass.

    But shouldn’t the mass-loss-process be reversed if the positive energy particle falls in towards the BH and the negative energy one streams away from the BH?


  39. Sabine,

    I said it would be controversial! The Hoyle example was just to make the logical point that there is a conceptual difference between retrodictabiliy and physical reversibility, at least in the sense that we say in classical thermodynamics that everything is fundamentally reversible, and so the Second Law is not a strict physical law. In thermo, the discussion is about physical reversibility, and in evaporation it is about retrodictability (can you logically recover the pre-evaporation state from the post-evaporation state, not can you physically "unevaporate" (which I guess would involve absorbing anti-Hawking radiation?)).

    Anyway, that is how the problem is usually presented, because it is discussed as a breakdown of retrodictability: can I tell from, e.g., the state of the Hawking radiation what fell into the black hole?

    There are some important issues to discuss about just what one means by the post-evaporation state. Many people say that the real puzzle here is a pure-to-mixed transition from the pre- to post-measurement state, which is supposed to violate unitarity, and hence fundamentals of quantum theory. Presumably they have in mind an epistemic understanding of the mixed state: the mixed state is not the actual physical post-evaportation state, but rather some pure state, but different pure states in different cases. So it is really a pure-to-pure transition that is not deterministic: just like collapse. Another question is what one even means by the "post-evaporation state". In many presentations of the puzzle, this is very problematic, as what is referred to is the state on a non-catchy surface. But it is no surprise that the evolution from a state on a Cauchy surface to the state on a non-Cauchy surface loses information or is pure-to mixed. That is, the way the problem is often presented, there is no problem at all.

  40. Dear Sabine,

    You seem to be accepting the idea that measurements are irreversible in quantum mechanics, but there is almost a consensus against this idea -- a rare thing in the fractious field of quantum foundations.

    To make measurements actually irreversible you would need something different than unitary evolution to be physically happening, and the only people who actually defend that are the very few who believe in collapse models (like CST or GRW). Bohmians and Many-Worlders are happy to state outright that there is no irreversibility, and even Copenhageners baulk at defending actual collapse: they usually retreat into some vague stuff about collapse being only in your head, and the quantum state not being real in any case.

  41. Elver,

    No, virtual particles in a pair have both positive energy. It's a common misunderstanding though.

    They can have 'effectively' negative energy if they are 'holes' in a background (say, some kind of conductor) and the energy of the background can't change. That's where the idea comes from.

    This is also basically what happens in Hawking's calculation. However, I think it is much better to think of the production of particle pairs (both of positive mass/energy) as taking energy from the background. Imo, this makes much more sense physically, though it isn't (yet!) quite backed up by math (the problem being that it's difficult to define what's the energy of the gravitational field). It's easier to understand this if you think of electric fields. In a strong enough electric field, virtual particle pairs (of charged particles) can be ripped apart. The energy for this is taken from the background field.



  42. MustNotBeBlank,

    I don't understand what you mean by the black hole information loss problem being different from quantum measurement. I said that the problem exists already if you don't make any measurement. Best,


  43. Unknown,

    I'm not "accepting" any of that sort, I'm merely answering the question I was asked.

  44. Sabine,

    Sorry I wasn't more clear. I was commenting on your statement that quantum measurement is irreversible. If so, the measurement process itself is fundamentally irreversible and black hole evaporation is no longer the only process that is fundamentally irreversible. I think it may have been better to discuss how quantum measurement is not necessarily irreversible at all and being much closer to thermodynamic irreversibility.


  45. Sabine,
    I guess it would help to actually ask the question. (And yes, I think it has to do with the black hole information paradox)

    Given a nonrotating spherical body that collapsed to a black hole. At coordimate time t1, at radius r1, the time a signal needs to an observer in the vacuum outside the black hole is infinite, while at any greater radius it is still large but finite. Does that mean at t1, the event horizon is defined to be at r1?

    Another question: Birkhoffs theorem appears to say frame dragging in the radial direction in the vacuum outside such a black hole is zero. Can that be generalized to state there is no radial frane dragging there in general? (With rotating masses, I think the transversal frame dragging would eventually sink to miniscule values, but never actually to zero)

    If both answers are "yes", then I think the information doesn't get destroyed since the mass never enters the singularity in the first place. (It only would if the black hole would never evaporate at all)

  46. You remark that the singularity is hidden behind the horizon and does no harm. But if you make it through the horizon dont you get crushed in it. Sounds like harm to me.

  47. Ambi Valen,

    The coordinate time it takes a signal to reach infinity is infinite, regardless of where it's emitted. A signal emitted from the horizon doesn't reach infinity (not in infinite coordinate time either).

    I don't know what frame dragging has to do with any of this. You seem to erroneously come to the conclusion that nothing can fall into a black hole. This is wrong. I recommend you look at the causal diagram, that should answer all your questions.

  48. John,

    Ha. Yes, it would be decidedly unpleasant. What I meant was that the singularity in GR doesn't lead to any contradictions. It does no 'mathematical harm' so to say.

  49. MustNotBeBlank,

    As I said, the problem already exists before a measurement has been made, so what you say is irrelevant.

  50. Sabine, great article . Again would like your opinion on two recent papers:

    (The punchline of this paper is that pulsar timing data has already ruled out any BSM physics beyond QG scale.
    If so, people should just forget about LHC, ILC etc)

    o Recent paper on Riemann hypothesis

  51. Shantanu,

    1st paper's on the reading list already. 2nd paper I'm not going to comment, it's out of my field of expertise (and, admittedly, I'm not very interested either).

  52. Sabine,
    I've liked black holes in science fiction since I was young. However, once I started to understand gravity doesn't suck things in but curves space, a problem appeared. If matter and light are just accelerated, and stronger the closer to the mass they are, black holes aren't a problem.

    But in general relativity, light and matter are not accelerated but follow the geometry of the curved spacetime. How can it then happen that from the same point in spacetime matter can travel inwards, but light, which is faster then matter, cannot travel outwards? (And I do mean in the standard coordinate system, not the comoving one.) I thought I found the answer in frame-dragging which is proven to exist around rotating black holes (but in lateral direction there).

    But last year, I became convinced that doesn't work either, and arrived at the caveman version of Oppenheimer's result, and thought that matter cannot enter a black hole.

    Turned out I simplified the situation too much, and took at idealised special case as the general answer. In the real world, this special case doesn't apply anyway, as black holes are slowly but continuously gaining mass and expand, so anything that falls towards one will cross the event horizon after finite coordinate time.

    So right now I am now convinced that matter falls into the black hole, but not convinced that it arrives in the singularity before the black hole evaporates.

    (I'm not 100% sure I'm using the correct terminology here. I mean light - or information in general - emitted from the falling particle will in one moment in coordinate time take finite coordinate time to an observer outside the object - e.g. in 1 light second distance - while in the next moment it would need infinite coordinate time. Is the border passed between those moments in coordinate time the event horizon, or is another term used here?)

    As for the causal diagram, I didn't find it helpful. I'm looking for a different kind of diagram, with standard coordinate time on one axis and radial standard coordinate distance on the other, with graphs showing the movement of radially infalling particles over time.

  53. One issue that I'm surprised no one brought up yet: if all the information has to come out from a tiny remnant, doesn't that violate the Bekenstein bound as ordinarily understood?

  54. Scott,

    That's right. I didn't want to go into it here because the blogpost was getting too long already, but I explained this here (and it's also, of course, in the above mentioned paper with Lee). If the information comes out late, then one has only the weak form of the Bekenstein-Hawking entropy (in which the entropy does not count the the internal states of the black hole but is merely a placeholder for a thermodynamical description used by the outside observer). Best,


    1. Ok, but that's a pretty important point for me, because it's precisely where I get off the remnant train and onto the Susskind one. If you believed that entropy has to count internal states of the black hole, then you'd also believe that the information loss problem wasn't solved in the 70s or early 80s, and that the last few decades of research on complementarity, AdS/CFT, firewalls, etc etc might not have been in vain, correct?

  55. Hi Sabine, One version of the paradox I am aware of is that according to the classical theory of black holes an object (which can be a photon, and is usually referred to as “Alice”) can pass through the event horizon of the black hole, never to return. But when you add quantum mechanics considerations you are driven to the conclusion that the event horizon itself represents some sort of singularity, or in other words, Alice will burn up passing through it. This is based on the fact that the same particle cannot be in entanglement with two different particles. (I am also aware with the version of the paradox that Alice will eventually evaporate and all its quantum information will be lost, in contrast to the reversibility of quantum mechanics. which seems the version you discuss in the post.) Are these two versions of the paradox equivalent in some sense? In particular, is your proposed solution with Lee Smolin also explains the version about Alice being burned passing through the event horizon?

  56. Dear Dr. B.
    You write
    "You seem to erroneously come to the conclusion that nothing can fall into a black hole. This is wrong."

    I know that an observer falling in obviously will cross the horizon and hit the singularity in finite time (of the observer).

    However, I have seen explanations that say that an outside observer never sees objects cross the horizon. Time is observed to stop on the horizon, as seen from the outside. As the black hole will eventually evaporate in finite time, the infalling object would evaporate in this view, before it would cross the horizon.

    In this view, there is no information paradox for an observer on the outside, as nothing is ever seen to cross the horizon. Something comparable was argued from the view of the invalling observer.

    In this account, the problems only appeared when evaporated information falls into the black hole again, leading to a kind of quantum entanglement doubling,

    I am unable to combine this account with your description. I am also unable to find faults in either account.

    Could you explain what is wrong with this account I describe?

  57. gilkalai,

    No, what you're referring to isn't the black hole information loss problem, but the so-called firewall problem, which isn't a problem but just a mathematical mistake.

  58. Scott,

    Not sure I parse your comment correctly, but it's right that string theory supports the idea that the black hole entropy counts microstates which is in conflict with the weak interpretation of the BH entropy and hence doesn't seem to square with remnants.

  59. Rob,

    The outside observer never sees objects crossing the horizon if the black hole does not evaporate. If it evaporates, the observer will eventually see the object crossing (though the notion of horizon maybe somewhat different).

  60. Sabine: "the so-called firewall problem, which isn't a problem but just a mathematical mistake." Sabine, please do explain or give links (or both) why do you regard the firework problem as simply a mathematical mistake. (It looks that much effort is devoted to discuss and understand this problem, and to relate it to a lot of interesting things.)

  61. gilkalai,

    I wrote about this here.

    The supposed problem of the firewall rests on a proof that allegedly shows that four assumptions are mutually inconsistent, ie at least one of them must be dropped for the rest to be consistent. All the literature that has followed afterwards is about which assumption is to be dropped.

    To begin with if the information is released late (if you have remnants) then one of these four assumptions doesn't apply so there's no firewall problem either.

    What's more perplexing though is that the proof itself is wrong: What makes the four assumptions incompatible is a fifth assumption that enters somewhere in the text. I explained this already in a comment in 2012, but nobody paid any attention. I then wrote a paper with an explicit counterexample (and it's published and all). But well, you see, it doesn't matter because nobody wants to hear it - it would just mean no more papers about the topic.

    The one thing that makes me feel better is that Gerard 't Hooft has a proposal that I believe is related to mine (though I think he doesn't think so) and nobody's paying any attention to him either.

  62. We'll have to dig up the old cliche then once again :

    " A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. "

    Max Planck

    Best, Koenraad

  63. Dear Sabine,

    I am not following quite your terminology here. As I understand the term, if there is a remnant then it is not that "the information comes out late" but that the information does not "come out" at all. (You can make sense of "come out" by reference to the sort of Penrose diagram that has en evaporation event and a proper event horizon of the evaporating black hole.) Can you explain just what you mean by a remnant?

    I take the idea of a remnant to be one that still has a singularity, not a proposal that "cures" the singularity. In the latter case, then in the normal sense no black hole ever forms at all, hence there is no event horizon in the proper sense. I take it that is what you refer to by "(though the notion of horizon maybe somewhat different)" above. Could you say a few words about that? If the singularity is cured, then the notion must be different, yes? So what is the notion?

    If the singularity is cured, and there is no black hole at all (in the proper sense), then there is no problem to be solved. At least not about reversibility or unitarity. It is exactly here that sloppy references to "information", "amounts of information" and "location of information" (as in "the information falls with Alice through the horizon") come to the fore, together with the introduction of talk of entropy (which is no part of Hawking's original argument).



  64. Tim,

    For that very reason I carefully avoided using the word 'remnant' in my blogpost! It goes in the literature under the name 'remnant solution' but this is a misnomer. The reason for the naming is that it's taken as settled that in the case when the solution comes out late the remaining state must be very long lived. It's hence either eternal (an actual remnant, sometimes also 'relic') or it decays only after a very long time (a quasi-stable remnant). Problem is that this conclusion already relies on the interior volume being small, hence I think it's wrong. Best,


  65. Thanks for that...can you also explain, or point a place, about the changed notion of a horizon in this case, and what time is meant in "after a very long time". Coordinate time in some coordinate system?

  66. Interesting stuff Sabine. Particularly after reading your Nature commentary.

  67. Regarding the difference between BH information paradox and quantum state collapse by measurement. I would say that in one measurement setting, the collapse is from one pure state to another pure state, but not via a unitary evolution. For BH information paradox, it is evolution of a pure to a mix state in one setting (i.e. one black hole). In technical jargon, it becomes an improper mixture, whereas repeated quantum measurements result in proper mixture i.e. final state of system is still pure after each run. (We do not go into the entanglement between apparatus and system here.)

    Also, BH information paradox should be clearly separated by another apparent information problem, which is the state of a BH is much simpler to describe than that of the total matter that collapsed into it. This I think might be due to the informations reside inside BH.

    But I have a question, what about the proposal that matter falling into BH come out from white hole in another region (or universe)?

  68. Tim

    I explained the difference between eternal and apparent horizon here. Regarding lifetime, well, that depends on the amount of information you have to get out. Seeing that there's no bound on what might be in, it could be arbitrarily large. About how fast it comes out, there are some estimates... I believe the most accessible one might be in a paper by Page some time in the mid 90s. I'll have to look up the reference. (Will post later.)

  69. Sabine,

    thanks for the link to "If it quacks like a black hole". I think I'm mostly in agreement to what's written there, and if I understood things correctly, I support your conservative scenario 3.

    What I'm not sure about is if there are disagreements to the following paragraph: "It is very unfortunate that this statement by Hawking has been misinterpreted in this way because there are in fact people who claim that black holes don’t exist. They argue that what we observe are actually just very dark massive objects that never collapse beyond their Schwarzschild radius, but they do have a material surface. This is a fringe opinion to say the least, because it requires substantial changes to Einstein’s theory of gravity, not to mention that it’s in conflict with observation. I am very sure this is not what Hawking was referring to."

    What did you mean with "this" in "This is a fringe opinion"? I would agree there is no material surface in the usual static way with matter cashing onto the surface. But I would also say that there is only collapse towards the Schwarzschild radius in standard coordinate time, not beyond it.

    I think this doesn't have to be a contradiction - the original collapsing body's surface collapses towards the original body's Schwarzschild radius, but the black hole continuously gains mass from outside (from matter around, or from its accretion disk, or at the very minimum from background radiation). So the original body's surface soon finds itself below the new Schwarzschild radius corresponding to the black hole's grown mass, and from then on, the curvature strengthened by the new mass outside the original surface will soon prevent signals from the original surface escaping.

    Does this viewpoint have any supporters, or even an official name?

  70. Trying to clarify: "the info comes out late" refers not to what you & Lee called "strong form" entropy, but more like your "weak form". So, microstates vs. observables. E.g., a distant observer gathers up all the Hawking radiation & tests for correlations. To reconstruct the 1st bit, you have to wait for half the mass to evaporate. The so-called Page time. Decoding then speeds up exponentially since we don't start from scratch. This kind of "late info" says nothing about the underlying microstates. Strong form entropy orthodoxically goes down by d(M^2) with every Hawking quantum. Speaking of which, the reason this orthodoxy disregards your rebuttal to Lenny's paper is you didn't directly address the meat of the argument, but instead took a blanket contrarian position that to them is heresy violating what they hold as the 1st law of BH thermo. It looks inconsistent to accept the negative mass of infall Hawking partners without drawing the required direct reduction in microstates. They'd probably toss your paper in the bin immediately on reading that. IMO, what's going on with that pair production description is an attractive explanation that avoids having to admit it amounts to tunneling.

    Of course the strings community believes that the various plausibility arguments, including the string theory confirmation for extremal BHs, support their ideas on BH thermo. While speculative, as long as the story hangs together, it's viable & they can pursue it. You're right to be skeptical, but their position makes sense. We can't just blame this all on bias. With a grain of salt as IANAP. Rgds,

  71. Mike,

    I agree with what you say. Of course they did toss the paper in the bin. Of course I think we'll end up being right. Let me add that the distinction between the 'strong' and 'weak' interpretation of the BH entropy didn't come from us, though I don't know where it originated.

  72. Ambi Valent,

    I mean that pretty much nobody believes it's consistent with GR. I'm referring to gravastars and similar things. I believe this is a misunderstanding, your further comment makes me think you had something else in mind.

  73. Sabine, thanks for the explanation --Gil

  74. Hi Sabine,

    You wrote "irreversible processes however don’t exist in quantum field theory" and "entropy increase usually does not imply a fundamental irreversibility, but merely a practical one".

    How do we know irreversibility is wrong? If we abandon the assumption of reversibility, does this make the black-hole information paradox go away?

    What goes wrong if we assume that Lindblad evolution is fundamental (rather than approximately expressing the behaviour of subsystems of larger systems undergoing Schrodinger evolution)?


  75. Richard,

    You can't just 'abandon' irreversibility. It's deeply built into quantum field theory. You'll have to rewrite the whole theory - and do that without ruining any of its achievements.

  76. Sabine,

    apparently I was too long-winded... so a much shorter question: In that Hawking quote: “The absence of event horizons mean that there are no black holes – in the sense of regimes from which light can’t escape to infinity.” does Hawking mean with "escape" that the particles and photons still exist beyond the horizon and are eventually freed (that's what I thought he meant)?

    Or would "escape" include the original particles and their properties being destroyed when entering the singularity and new particles being created when the singularity finally dissolves at the end of a black hole's existence?

  77. Personally, i don't worry about it,i can not be consumed by nonsense,Black Hole Information and it's paradoxes should only be seen in children's books.

  78. Sabine,

    Thanks for mentioning that abandoning reversibility is not easy to do in quantum field theory.

    As a computer scientist whose knowledge of QM is in the context of quantum computing (admittedly ignorant of QFT), I'd like to try to understand what fundamental problem arises. If we try to express QFT in terms of Markovian (Lindblad) evolution to encompass black hole evaporation, what goes wrong? I know I'm way out of my depth here. Can anyone point me to an accessible reference related to this?

    Richard (Cleve)

  79. Richard,

    What's the Lindblad operator, where does it come from, what happens to Lorentz-invariance, how come we've never noticed any of that? The problem is: The Standard Model of Particle Physics is an extremely precisely tested theory. You can't just change something about it and hope to still reproduce all predictions.

  80. Ambi Valent,

    He probably doesn't mean that it's the same particles that come out, because they will interact with each other and so on, but that they continue in a 'normal' QFT time evolution (ie with a Hamiltonian operator). If you want to speak about 'existence' I can't help unless you give me a definition for 'existence'. Best,


  81. Hi Sabine,

    Thank you for your great posts. Actually measurement process is non unitary mapping pure states into mixed ones, at least not considering decoherence. So adding a few axioms to qft like the measurement ones it should be possibile to have a theory which behaves like a qft with at low energies but it's not always unitary, especially when dealing with gravity. What do you think? Are there any paper in this direction? Maybe it's nonsense :)


  82. Sabine, I could not find any mention in your article or the comments of this 2015 paper by Thiago Guerreiro and Fernando Monteiro. According to this brief overview by Viktor Toth, it purports to "solve" the paradox by showing that nothing can ever reach the event horizon. Had you found reason to dismiss this paper? (Or just not enough time to read all papers while replying to these 85 comments?)

  83. Andy,

    The paper's wrong and should not have gotten published. Read this and comments on this post.

    There are a couple of other papers that have made similar claims. They're also wrong, though each for other reasons. Some have a wrong definition of temperature. Others screw themselves over with asymptotic limits. The best way to deal with that is to realize that there are literally hundreds of textbooks and lecture notes that prove stuff can fall through the horizon.


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