Monday, October 26, 2015

Black holes and academic walls

Image credits: Paul Terry Sutton
According to Einstein you wouldn’t notice crossing a black hole horizon. But now researchers argue that a firewall or brickwall would be in your way. Have they entirely lost their mind?

Tl;dr: Yes.

It is hard, sometimes, to understand why anyone would waste time on a problem as academic as black hole information loss. And I say that as someone who spent a significant part of the last decade pushing this very problem around in my head. Don’t physicists have anything better to do, in a world that is suffering from war and disease, bad grammar even? What drives these researchers, other than the hope to make headlines for solving a 40 years old conundrum?

Many physicists today work on topics that, like black hole information loss, seem entirely detached from reality. Black holes only succeed in destroying information once they entirely evaporate, and that won’t happen for the next 100 billion years or so. What drives these researchers is not making tangible use of their insights, but the recognition that someone today has to pave way for the science that will become relevant in a hundred, a thousand, or ten thousand years from now. And as I scan the human mess in my news feed, the unearthly cleanliness of the argument, the seemingly inescapable logic leading to a paradox, admittedly only adds to its appeal.

If black hole information loss was a cosmic whodunit, then quantum theory would be the victim. Stephen Hawking demonstrated in the early 1970s that when one combines quantum theory with gravity, one finds that black holes must emit thermal radiation. This “Hawking radiation” is composed of particles that besides their temperature do not contain any information. And so, when a black hole entirely evaporates all the information about what fell inside must ultimately be destroyed. But such destruction of information is incompatible with the very quantum theory one used to arrive at this conclusion. In quantum theory all processes can happen both forward and backward in time, but black hole evaporation, it seems, cannot be reversed.

This presented physicists with a major conundrum, because it demonstrated that gravity and quantum theory refused to combine. It didn’t help either to try to explain away the problem alluding to the unknown theory of quantum gravity. Hawking radiation is not a quantum gravitational process, and while quantum gravity does eventually become important in the very late stages of a black hole’s evaporation, the argument goes that by this time it is too late to get all the information out.

The situation changed dramatically in the late 1990s, when Maldacena proposed that certain gravitational theories are equivalent to gauge theories. Discovered in string theory, this famed gauge-gravity correspondence, though still mathematically unproved, does away with the problem because whatever happens when a black hole evaporates is equivalently described in the gauge theory. The gauge theory however is known to not be capable of murdering information, thus implying that the problem doesn’t exist.

While the gauge-gravity correspondence convinced many physicists, including Stephen Hawking himself, that black holes do not destroy information, it did not shed much light on just exactly how the information escapes the black hole. Research continued, but complacency spread through the ranks of theoretical physicists. String theory, it seemed, had resolved the paradox, and it was only a matter of time until details would be understood.

But that wasn’t how things panned out. Instead, in 2012, a group of four physicist, Almheiri, Marolf, Polchinski, and Sully (AMPS) demonstrated that what was thought to be a solution is actually also inconsistent. Specifically they demonstrated that four assumptions, generally believed by most string theorists to all be correct, cannot in fact be simultaneously true. These four assumptions are that:
  1. Black holes don’t destroy information.
  2. The Standard Model of particle physics and General Relativity remain valid close by the black hole horizon.
  3. The amount of information stored inside a black hole is proportional to its surface area.
  4. An observer crossing the black hole horizon will not notice it.
The second assumption rephrases the statement that Hawking radiation is not a quantum gravitational effect. The third assumption is a conclusion drawn from calculations of the black hole microstates in string theory. The fourth assumption is Einstein’s equivalence principle. In a nutshell, AMPS say that at least one of these assumptions must be wrong. One of the witnesses is lying, but who?

In their paper, AMPS suggested, maybe not quite seriously, giving up on the least contested of these assumptions, number 4). Giving up on 4), the other three assumptions imply that an observer falling into the black hole would encounter a “firewall” and be burnt to ashes. The equivalence principle however is the central tenet of general relativity and giving it up really is the last resort.

For the uninitiated observer, the lying witness is obviously 3). In contrast to the other assumptions, which are consequences of theories we already know and have tested to high precision, number 3) comes from a so-far untested theory. So if one assumption has to dropped then maybe it is the assumption that string theory is right about the information content of black holes, but that option isn’t very popular with string theorists...

And so within a matter of months the hep-th category of the arxiv was cluttered with attempts to reconcile the disagreeable assumptions with another. Proposed solutions included everything from just accepting the black hole firewall to the multiverse to elaborated thought-experiments meant to demonstrate that an observer wouldn’t actually notice being burnt. Yes, that’s modern physics for you.

I too of course have an egg in the basket. I found the witnesses all to be convincing, none of them seemed to be lying. And taking them at face value, it finally occurred to me that what made the assumptions seemingly incompatible was an unstated fifth assumption. Like witnesses’ accounts might suddenly all make sense once you realize the victim wasn’t killed at the same place the body was found, the four assumptions suddenly all make sense when you do not require the information to be saved in a particular way (that the final state is “typical” state). Instead the requirement that energy must be locally conserved near the horizon makes the firewall impossible and at the same time also told me exactly just how the black hole evaporation remains compatible with quantum theory.

I think nobody really liked my paper because it lead you to the rather strange conclusion that somewhere near the horizon there is a boundary which does alter the quantum theory, yet in a way that isn’t noticeable for any observer near by the black hole. It is possible to measure its effects, but only in the far distance. And while my proposal did resolve the firewall conundrum, it didn’t do anything about the black hole information loss problem. I mentioned in a side-note that in principle one could use this boundary to hand information into the outgoing radiation, but that would still not explain how the information would get into the boundary to begin with.

After publishing this paper, I vowed once again to never think about black hole evaporation again. But then last month, an arxiv preprint appeared by ‘t Hooft. One of the first to dabble in black hole thermodynamics, in his new paper ‘t Hooft proposes that the black hole horizon acts like a boundary that reflects information, a “brick wall” as New Scientist wants it. This new idea has been inspired by Stephen Hawking’s recent suggestion that much of the information falling into black holes continues to be stored on the horizon. If that is so, then giving the horizon a chance to act can allow the information to leave again.

I don’t think that bricks are much of an improvement over fire and I’m pretty sure that this exact realization of the idea won’t hold up. But after all the confusion, this might eventually allow us to better understand just exactly how the horizon interacts with the Hawking radiation and how it might manage to encode information in it.

Fast forward a thousand years. At the end of the road there is a theory of quantum gravity that will allow us to understand the behavior of space and time on shortest distance scales and, so many hope, the origin of quantum theory itself. Progress might seem incremental and sometimes history leads us in circles, but what keeps physicists going is the knowledge that there must be a solution.

[This post previously appeared at Starts with a Bang.]


  1. I guess I don't really understand the black hole information paradox. If the black hole distorts time so that from the outside perspective nothing ever passes the event horizon then no information can be lost. It comes out when the final evaporation of the black hole blasts into it before it ever crosses the event horizon. It hits a literal fire wall. This is in principle observable but... unsafe.

    Maybe you could think of the event horizon and the singularity as two different ways to view the same object. And the collision with the fire wall and the collision with the singularity is two different ways to see the same event.

  2. Maybe the Event Horizon Telescope will cast some light on this.

  3. Dear Bee,
    Is your black hole near-the-horizon-boundary-condition something like boundary conditions that rule out unphysical solutions of the second-order partial differential equations of classical physics? Or is there some new physics it is hinting at?

  4. Hallo - I progressively get the feeling that one of the actual difficulties in that advanced research comes from the fact that one stays at a very theoretical and abstract level and that one is not enougth confronting the theories (academy) with new and recent informations coming from, e.g. cosmological observations. For example: how can one discuss about BH without including considerations inherited from the condensed matter physics and/or from knowledge concerning neutrons stars, superfluids, constrainted spins and so on?

    Just to -perhaps- open the debate.

  5. H1821+643 central quasar black hole, 3×10^10 solar masses, 9×10^13 meters radius. An entering free fall observer sees no local surface curvature, field gradient or divergence; (6×10^43 g)/(3x10^48 cm^3) = 2×10^(-5) g/cm^3 internal average. Air is 1.2×10^(-3) g/cm^3.

    "Einstein’s equivalence principle" Einstein–Cartan–Sciama–Kibble theory offers geometric EP tests via chemistry, 0.1 nm^3 single molecules to kilogram 3-D tessellation self-similar periodic single crystals. Physics has unproductively contrasted everything else. PSR J1903+0327 and PSR J0348+0432: gravitational binding energy, magnetic field, superconductive protons and superfluid neutrons vs. hydrogen plasma or Fermi-degenerate iron, extreme isospin and lepton number divergences, 11% of lightspeed equatorial spin velocity.

    "Fast forward a thousand year[s]."
    90 days. Look orthogonal to the box.

  6. Which part of yours? We just had a talk by Mathur about fuzzballs. I'd like to see your thoughts on this some Monday.

  7. Also, in the t'Hooft's paper it is not clear how gravitational interaction can carry QM information such as spin.

  8. ppnl,

    It takes a finite time to cross the event horizon, not an infinite time. Stuff does fall in. That it takes a long time for the distant observer to see is entirely irrelevant. Also, if the black hole evaporates it doesn't actually take forever. Saying "it does come out with the final evaporation" doesn't solve the problem because it doesn't explain how it comes out. There are some arguments (imo not very convincing) that the information can't come out in the late phases because not enough energy is left. Best,


  9. Thierry,

    Well, I agree to some extent, thus the title of my post. Having said that, I don't know why you think neutron stars are relevant for the black hole information loss problem. It is true that you can try to use condensed matter physics to address the problem by means of emergent gravity or by means of dualities. This is a very active area of research. Best,


  10. Perry,
    Not a big fan of fuzzballs. I wrote a paper with Lee in 2009 (you'll find it on the arxiv) in which we said that the most obvious solution is still the best one, and I still think this is correct. There isn't any good reason why the information shouldn't just stay with the black hole and be released in the strong curvature phase. If you think that remnants are a problem, I encourage you to dig out the references on which these supposed problems are based (we quote them in our paper). The main reason, I believe, that people don't like this option is that it rests on the weak interpretation of the bh entropy. Having said that, fuzzballs require strong modification at horizon size. I don't see a good justification for that. Best,

  11. Arun,

    The boundary condition is a consequence from having picked the initial vacuum state (pure) and the final vacuum state (which you want also pure). You can't chose it freely. You could use the boundary condition to select 'good' solutions if you start with the initial state only - but that's not how people have looked at this problem.

    It is quite similar to the idea of putting boundary conditions on the singularity, except that you don't need to do it at the singularity, which seems very contrived. You can do it just outside the horizon.

    Does it indicate new physics. Let me put it this way. This boundary condition is what you need to make these four assumptions work together. Sooner or later the rest of the physics-world will come around to realize that (or so I hope in my blue-eyed naivite). I think this would fit in well with AdS/CFT, but whether it's got something to do with the real world, I don't know. I actually don't think so. As I said in a comment above, I think the obvious solution is that the information gets out in the final state, and I don't think any of the arguments that have been brought up against this obvious solution are convincing. Best,


  12. "bad grammar" ... "thousand year" :-|

    Should be "years", of course.

  13. "Specifically they demonstrated that four assumptions, generally believed by most string theorists to all be correct, cannot in fact be simultaneously true."

    Is this result completely robust? As true as a theorem can be?

  14. Phillip,
    The point of my paper was to demonstrate that it is not robust... Best,

    PS: Fixed the typo :)

  15. OK, that is the "unstated fifth assumption", so if that assumption is not justified, then the tetralemma (bull with four horns) dissolves. But with the fifth assumption, is the statement that not all four can occur robust in the sense of a mathematical proof?

    Yes, I will read the paper in detail but want to make sure I read it in the right way. :-)

  16. Is a Black Hole not just another brick in the wall?


  17. "It takes a finite time to cross the event horizon, not an infinite time."

    I don't understand this and am not sure there is not some misunderstanding.

    My understanding is that for a distant observer an object can never be seen to cross the event horizon because time will slow to the point of stopping at the horizon. If you could ever get to the horizon. Which you can't because time keeps slowing enough to prevent you from ever getting there.

    My understanding is that an observer falling in would see themselves crossing the horizon and reaching the singularity very quickly.

    A quick check of stack exchange seems to reinforce my understanding.

    So I don't understand how a distance observer can see a crossing of the event horizon. What am I missing?

  18. ppnl,

    An infalling observer crosses the horizon at finite time. If the black hole is eternal, this crossing happens at infinite time for the distant observer. If the black hole evaporates, it happens at finite time. Best,


  19. Phillip,

    I think so, yes, provided you use the exact mathematical definitions for the four assumptions that were used in the paper. This pulls after it some interpretational questions, notably it is very untrivial to find out exactly what the observer would actually observe, and the quantities used in the paper are not actual observables. One can try to pick at this point, and in fact some other people have done that. Best,


  20. " An infalling observer crosses the horizon at finite time. If the black hole is eternal, this crossing happens at infinite time for the distant observer. If the black hole evaporates, it happens at finite time. "

    Ah ok, that is what I am missing. Thanks. Yet I cannot see how since time must always stop at the horizon. I have not found an explanation for this yet.

  21. ppnl:

    If the black hole entirely evaporates it does not, in most cases, have an eternal horizon.

    If you really want to understand the black hole information loss paradox, I highly recommend you have a go at Causal diagrams. Once you understand the causal structure things become dramatically clearer. Best,


  22. Two layperson questions:

    1. Why is the information loss problem a quantum one? Even in classical physics, black hole creation is a non-reversible process. And information is lost when a black hole is created since a classical black hole only has 3 degrees of freedom if I understand the no-hair theorem correctly.

    2. What is an event horizon in a theory which allows black holes to evaporate? In GR, the event horizon depends on global conditions, it's not something that depends on the current black hole mass but also for incoming matter that will increase the radius in the future.

  23. 1) If the black hole doesn't evaporate, there's no problem because the black hole could just keep information forever. The problem becomes only apparent once it can evaporate, because if it entirely evaporates, the information must be lost. Without quantum effects, no evaporation, no problem.

    2) If the black hole evaporates, in most cases there's no eternal event horizon but only a temporary apparent horizon. There can still be an eternal horizon, it depends on how the evaporation proceeds. Remnant solutions typically have eternal horizons still.

  24. Thanks for the reply, and for this blog in general. It communicates cutting edge research extremely clearly.

    Wrt my second question, what I meant is: if there is no eternal horizon, at what point will in-falling matter encounter a firewall if that theory were correct? It's possible to imagine a particle crossing the a horizon, then some Hawking radiation gets away, shrinking the black hole so that the particle is outside again, and the particle falling in again. This is similar to the Voyager spacecrafts exiting the heliosphere several times.

  25. "Don’t physicists have anything better to do, in a world that is suffering from war and disease, bad grammar even?"
    What do physicists have to do with suffering from war and disease, or bad grammar? How is a specific subject within physics not worth our time because of more "pressing" problems? I certainly hope you were employing hyperbole. Or perhaps you're starting your article with a sort of sarcastic premise, as you seem to conclude the article by implying it's a worthy endeavor after all. I like your article (I stumbled upon your blog a few weeks ago as I was doing more research on black holes and have been reading some of your articles since), but the beginning put the article in an improper context as far as I'm concerned. Throughout the article I kept wondering why you made such an embarrassing argument, and why, if indeed it's such a fruitless endeavor, you're implying the whole matter of the black hole information paradox has actually refined some aspects of string theory and of physics in general. It wasn't until the end of the article that I suspected you were being sarcastic, but I still can't be sure.

    "There can still be an eternal horizon, it depends on how the evaporation proceeds. Remnant solutions typically have eternal horizons still."
    Are you suggesting parts of black holes remain like empty shells?

    I'm quite fascinated by 't Hooft's proposal that the black hole horizon acts like a boundary that reflects information. The more recent proposals of solutions to the black hole information paradox are quite interesting, though they seem exceedingly less likely. Are there other cases at all where information is reflected or is this a black hole novelty?

    I also get the feeling physicists aren't always equally serious in their proposals. I notice sometimes they make a proposal for completeness' sake rather than because they think it has merit. Is this a fair conclusion at all? I suppose it's a proper approach in any case. It may generate a lot of noise in science, but potentially a lot of insight as well.

    I've also been wondering, if black holes lose mass through thermal radiation, what prevents a black hole from becoming a neutron star? Wouldn't there be a point where so much mass has radiated away that space around the object no longer curves to such extent that photons become trapped?

    PS: If you want to type 't Hooft's name, I recommend first typing an arbitrary letter, then the apostrophe, then remove the letter and then type out the rest of the name. If you just type apostrophe + t , your apostrophe will be upside down. One might argue "Don't typographers have anything better to do?", but really, it's quite frustrating to me to see his name being improperly mentioned constantly. To someone's amusement presumably he might be making the same mistake with his own name. Digital typography is incredibly clumsy.

  26. Martin,

    I think it is a question that we should ask ourselves every once in a while: is this a good investment of money. I hope you read enough of my article to realize that I am arguing the answer to this question is yes. The mentioning of 'bad grammar' should have been a hint that I wasn't being too serious. Best,



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