[Illustration of black hole. Image: NASA] 
Before Hawking, black holes weren’t paradoxical. Yes, if you throw a book into a black hole you can’t read it anymore. That’s because what has crossed a black hole’s event horizon can no longer be reached from the outside. The event horizon is a closed surface inside of which everything, even light, is trapped. So there’s no way information can get out of the black hole; the book’s gone. That’s unfortunate, but nothing physicists sweat over. The information in the book might be out of sight, but nothing paradoxical about that.
Then came Stephen Hawking. In 1974, he showed that black holes emit radiation and this radiation doesn’t carry information. It’s entirely random, except for the distribution of particles as a function of energy, which is a Planck spectrum with temperature inversely proportional to the black hole’s mass. If the black hole emits particles, it loses mass, shrinks, and gets hotter. After enough time and enough emission, the black hole will be entirely gone, with no return of the information you put into it. The black hole has evaporated; the book can no longer be inside. So, where did the information go?
You might shrug and say, “Well, it’s gone, so what? Don’t we lose information all the time?” No, we don’t. At least, not in principle. We lose information in practice all the time, yes. If you burn the book, you aren’t able any longer to read what’s inside. However, fundamentally, all the information about what constituted the book is still contained in the smoke and ashes.
This is because the laws of nature, to our best current understanding, can be run both forwards and backwards – every unique initialstate corresponds to a unique endstate. There are never two initialstates that end in the same final state. The story of your burning book looks very different backwards. If you were able to very, very carefully assemble smoke and ashes in just the right way, you could unburn the book and reassemble it. It’s an exceedingly unlikely process, and you’ll never see it happening in practice. But, in principle, it could happen.
Not so with black holes. Whatever formed the black hole doesn't make a difference when you look at what you wind up with. In the end you only have this thermal radiation, which – in honor of its discoverer – is now called ‘Hawking radiation.’ That’s the paradox: Black hole evaporation is a process that cannot be run backwards. It is, as we say, not reversible. And that makes physicists sweat because it demonstrates they don’t understand the laws of nature.
Black hole information loss is paradoxical because it signals an internal inconsistency of our theories. When we combine – as Hawking did in his calculation – general relativity with the quantum field theories of the standard model, the result is no longer compatible with quantum theory. At a fundamental level, every interaction involving particle processes has to be reversible. Because of the nonreversibility of black hole evaporation, Hawking showed that the two theories don’t fit together.
The seemingly obvious origin of this contradiction is that the irreversible evaporation was derived without taking into account the quantum properties of space and time. For that, we would need a theory of quantum gravity, and we still don’t have one. Most physicists therefore believe that quantum gravity would remove the paradox – just how that works they still don’t know.
The difficulty with blaming quantum gravity, however, is that there isn’t anything interesting happening at the horizon – it's in a regime where general relativity should work just fine. That’s because the strength of quantum gravity should depend on the curvature of spacetime, but the curvature at a black hole horizon depends inversely on the mass of the black hole. This means the larger the black hole, the smaller the expected quantum gravitational effects at the horizon.
Quantum gravitational effects would become noticeable only when the black hole has reached the Planck mass, about 10 micrograms. When the black hole has shrunken to that size, information could be released thanks to quantum gravity. But, depending on what the black hole formed from, an arbitrarily large amount of information might be stuck in the black hole until then. And when a Planck mass is all that’s left, it’s difficult to get so much information out with such little energy left to encode it.
For the last 40 years, some of the brightest minds on the planets have tried to solve this conundrum. It might seem bizarre that such an outlandish problem commands so much attention, but physicists have good reasons for this. The evaporation of black holes is the bestunderstood case for the interplay of quantum theory and gravity, and therefore might be the key to finding the right theory of quantum gravity. Solving the paradox would be a breakthrough and, without doubt, result in a conceptually new understanding of nature.
So far, most solution attempts for black hole information loss fall into one of four large categories, each of which has its pros and cons.
 1. Information is released early.
The information starts leaking out long before the black hole has reached Planck mass. This is the presently most popular option. It is still unclear, however, how the information should be encoded in the radiation, and just how the conclusion of Hawking’s calculation is circumvented.
The benefit of this solution is its compatibility with what we know about black hole thermodynamics. The disadvantage is that, for this to work, some kind of nonlocality – a spooky action at a distance – seems inevitable. Worse still, it has recently been claimed that if information is released early, then black holes are surrounded by a highlyenergetic barrier: a “firewall.” If a firewall exists, it would imply that the principle of equivalence, which underlies general relativity, is violated. Very unappealing.

2. Information is kept, or it is released late.
In this case, the information stays in the black hole until quantum gravitational effects become strong, when the black hole has reached the Planck mass. Information is then either released with the remaining energy or just kept forever in a remnant.
The benefit of this option is that it does not require modifying either general relativity or quantum theory in regimes where we expect them to hold. They break down exactly where they are expected to break down: when spacetime curvature becomes very large. The disadvantage is that some have argued it leads to another paradox, that of the possibility to infinitely produce black hole pairs in a weak background field: i.e., all around us. The theoretical support for this argument is thin, but it’s still widely used.
 3. Information is destroyed.
Supporters of this approach just accept that information is lost when it falls into a black hole. This option was long believed to imply violations of energy conservation and hence cause another inconsistency. In recent years, however, new arguments have surfaced according to which energy might still be conserved with information loss, and this option has therefore seem a little revival. Still, by my estimate it’s the least popular solution.
However, much like the first option, just saying that’s what one believes doesn’t make for a solution. And making this work would require a modification of quantum theory. This would have to be a modification that doesn’t lead to conflict with any of our experiments testing quantum mechanics. It’s hard to do.
 4. There’s no black hole.
A black hole is never formed or information never crosses the horizon. This solution attempt pops up every now and then, but has never caught on. The advantage is that it’s obvious how to circumvent the conclusion of Hawking’s calculation. The downside is that this requires large deviations from general relativity in small curvature regimes, and it is therefore difficult to make compatible with precision tests of gravity.
And it’s bound to remain so. The temperature of black holes which we can observe today is far too small to be observable. Hence, in the foreseeable future nobody is going to measure what happens to the information which crosses the horizon. Let me therefore make a prediction. In ten years from now, the problem will still be unsolved.
Hawking just celebrated his 75th birthday, which is a remarkable achievement by itself. 50 years ago, his doctors declared him dead soon, but he's stubbornly hung onto life. The black hole information paradox may prove to be even more stubborn. Unless a revolutionary breakthrough comes, it may outlive us all.
(I wish to apologize for not including references. If I’d start with this, I wouldn’t be done by 2020.)
[This post previously appeared on Starts With A Bang.]
36 comments:
can I say that blackhole radiation happense by breaking the entanglement of quantum objects/particles? That is, the nonlocality of quantum entanglement is violated at the event horizon.
is it possible that conventional quantum field theory is not valid BEYOND the Event Horizon as the singularity tears apart the entanglement of all objects/particles entering the (event horizon) of the black hole.
Dear Bee, thanks for the intresting information. But one point remains unclear. The fact is that from the point of view of a distant fiducial observer the black hole evaporates like any other body, e.g. a book. The observer has not any acces to the black hole interior. If the black hole was formed in a poor state then entanglement gradually transferes from the stretched horizon to the Hawking radiation. Where is there information loss?
Ivan,
" If the black hole was formed in a poor state then entanglement gradually transferes from the stretched horizon to the Hawking radiation."
How did the information ever get into the stretched horizon to begin with? And how is it being transferred? Not sure what problem you believe is solved by using semiplausible words.
Mars,
"can I say that blackhole radiation happense by breaking the entanglement of quantum objects/particles?
No, that's not correct. The correct statement is that hawking radiation *is* entangled (across the horizon). But that isn't the reason why it's created. It's created, to make a long story short, because the notion of 'particle,' like space and time, is relative.
is it possible that conventional quantum field theory is not valid BEYOND the Event Horizon as the singularity tears apart the entanglement of all objects/particles entering the (event horizon) of the black hole.
It's possible in the sense that nobody has been able to measure what happens beyond the horizon. However, it's hard to make any such modification without ruining GR and/or QFT in regimes that we have already tested. The singularity destroys half of the entangled particle pairs  that's the reason for the information loss. Best,
B.
Interesting post, Dr. B. But what I've never been able to understand is what the essential difference is to a black hole between a 1kg rock and a 1kg textbook. Or, alternatively, the difference between a 1kg collection of Shakespeare's sonnets and a 1kg book of chimpanzeeproduced gibberish. This seems to necessitate an intelligence aspect of infalling mass as far as the black hole is concerned.
laws of nature...can be run both forwards and backwards Submerge an Sshaped lawn sprinkler in a big bucket of water. Apply internal water pressure, it spins. Reverse time (aspirate), no spin.
the principle of equivalence[EP]...is violated. Very unappealing. Direct a vacuum supersonic expanded molecular beam (~1 kelvin rotational temperature) of 3:1 enantiomers 2cyanoD_3trishomocubane[1] through a chirpedpulse FT µwave spectrometer[2]. If rotational transitions are not sharpline, prolate symmetric top unified spectra, opposite shoes measurably violate the EP.
LIGO GW150914[3] observed 36 + 29 solar mass BHs inspiral, merge, emit 4.6% binding energy, then 0.05 second ringdown[4]. GW151226[5], 14.2 and 7.5 solar masses, 4.6% binding energy, 0.005 second ringdown[6]. There was no time for “interior” contents’ shuffling. Two soap bubbles touched, then popped into one. BHs are 2D+epsilon shells.
[1] DOI: 10.2174/138527212804004508, Scheme 50
[2] DOI: 10.1080/00268976.2013.793888
[3] https://losc.ligo.org/events/GW150914/
[4] http://www.soundsofspacetime.org/uploads/4/9/0/4/49047375/471920_orig.png
[5] https://losc.ligo.org/events/GW151226/
[6] http://ligo.org/science/PublicationGW151226/images/Fig5_v6.png
"How did the information ever get into the stretched horizon to begin with?"
From the point of view of a distant fiducial observer the black hole is nothing but the stretched horizon; the observer does not acces to the interior. So, if a black hole forms in a pure state then the stretched horizon (=black hoole!) must be in a pure state too. Entanglement occurs between different parts of the same horizon. If the black hole evaporates then the entanglement shifts from the stretched horizon to the outgoing Hawking radiation as in the case of a burning book.
Ivan,
Entanglement does not occur between different parts of the horizon, it occurs between particles of the radiation.
Dear Bee, if entanglement does not occur between different parts of the horizon (= black hole!), then the black hole is not in a pure state.
"If a firewall exists, it would imply that the principle of equivalence..."
or it would imply that the black hole is nothing but a bubble of nothing. That is, the event horizon is Witten's bubble of nothing that was formed in the center of a collapsing star due to vacuum instability of the KaluzaKlein vacuum, and which, after expanding out from the center, stabilized itself, under the strong pull of relativistic gravity, precisely at the event horizon, the Schwarzschild sphere.
Sabine,
Does Verlinde's (spelling?) entropic gravity ideas help out here at all?
Thanks,
Evan
Hi Sabine,
considering the time needed for evaporation, I wonder how much dark matter (particles) would fall there in the meantime. Any idea?
And how much of the standard (repulsive) scalar field should be trapped?
After all those two guys are supposedly energy like everything else.
Best,
J.
Bee,
I have the same Guess that information should be conserved, but what worries me is that I can't base that on anything.
I understand how conservation principles arise from Noether. Can you explain what symmetry is dual to "information"? You seem to be identifying it as timereversal, but the dual of that is not information (or not as I understand it), it is simply time parity. And that's not even Weakly conserved.
I can't even define information in this context well. It doesn't appear to be the microstate, because that's just counted by the BH entropy, and we understand that gets radiated away.
The missing bit seems to be that BHs have no means to maintain micro state. But that's in direct contradiction to the complaint that BHs are destroying information. Taking the infall out of the equation, where exactly is information being *created* to construct the Hawking radiation. It has still selected a definite end micro state out of the huge phase space open to it.
Could you help to define a couple of these points?
"This is because the laws of nature, to our best current understanding, can be run both forwards and backwards – every unique initialstate corresponds to a unique endstate"
From my "ancient" 2 quantum mechanics college courses, I still remember that QM interactions are random in nature, so we cant say anything about a specific outcome of an interaction, only probabilistic results, i.e., with many repetitions of exactly the same experiments, we can measure means, medians, standart deviation etc.
So what is the QM meaning of the above statement, that the laws can backward? the end state would lead to identical initial state only probabilistically, doesn't it?
Bill, there isn't any difference between a rock and a book as far as fundamental information is concerned, meaning the information required to describe the positions and velocities of the particles comprising the rock or book. The information in a written Shakespeare's sonnet is far less than the information required to describe the paper on which it is written.
Sabine,
"That’s the paradox: Black hole evaporation is a process that cannot be run backward. It is, as we say, not reversible."
My question is not about the physics, but about the wording. Isn't it "the falling of information into the black hole", rather than the evaporation of the black hole, which is the irreversible process?
Ivan,
What you say is wrong. A system does not need to have entanglement between different parts to be in a pure state. Besides this, the black hole isn't a quantum state in this treatment to begin with.
Indeed, the black hole is a bubble of nothing. It's defined by the causal properties of the spacetime. Best,
B.
Evan,
At first thought, no. At second thought, maybe. The reason is that a modification of gravity generally has the prospect of changing something about the way that black holes evaporate. I do not, however, presently see how Verlinde's approach could solve the problem. If you believe that it's a consequence of string theory, then of course it kinda has solved the problem already. Best,
B.
akidbelle,
Yes, one can estimate the accretion rate of dark matter (and other stuff) onto black holes (and neutron stars) etc, and one finds numbers somewhere in the literature. I don't know what this has to do with information loss however. Best,
B.
Hopefully,
That a process is reversible doesn't mean it's invariant under that reversal. Clearly the formation and subsequent evaporation of the black hole looks very different forwards than backwards. You shouldn't get hung up on the word 'information'. Forget about information. The black hole information loss paradox is that in a quantum field theory there's no irreversible process. Best,
B.
Miki,
You might also recall that the timeevolution is deterministic. There's a Hamiltonian operator. It can be run forwards and backwards. Not so with black holes. Best,
B.
Henry,
It's both together. A good way to think about it is to imagine some initial state in which the particles are very far away from each other and basically don't interact (the usual initial state in qft). They approach each other, collapse and form a black hole, the black hole evarporates. Particles disperse out to infinity again where they barely interact with each other. The timeevolution from the initial to the endstate is irreversible. Best,
B.
Bill,
The difference between these objects is in the way that the elementary particles are arranged relative to each other. That the black hole can't tell the difference is exactly the problem! Best,
B.
Thanks Bee, but I can still interpret this in two very different ways:
"Looks very different....irreversible" just sounds to me like standard second law thermodynamics. Put a book into BH, get Hawking radiation out, never observed Hawking radiation happening in a micro state corresponding to a book. True, but isn't that just a very low probability event? If this were not a BH and we were just putting stuff into a blender, it is strictly reversible. I don't *think* that is what is being said here.
I think what is meant is "there is no causal relation between the micro state of the book and the outgoing radiation". OK, then can we crack the problem into two, and actually look at the easier half  how can we explain that the entropy of the Hawking radiation has no causal relation to the "contents of" the BH. I can understand that as a central paradox.
And doesn't it help to exclude explanation #2  which wouldn't deal with that.
Does it also sort of link to Landauers limit  it costs entropy to erase a bit, but not to duplicate a bit, and there is no way to "create" a bit without violating causality.
Once again a delightfully informative blog post. Thanks a lot.
It seems to me that in principle the bookburning could also be irreversible once QM is included  but I see Miki Weiss has already stated that objection, and been answered that the evolution of the QM state via a Hamiltonian is deterministic. Which I guess means that once events have occurred the past is fixed, and running the equations backwards will reproduce it. (Why this is not also true for the random events of blackhole evaporation is not clear to me.)
But to take the smoke and radiation from the fire and reassemble it after the fire has occurred would be a new future which is not fixed and would contain new QM events, so actually the restoration of the information would not be possible, it seems to me, in principle.
Also there is the question of whether the calculus of time is true (i.e., time is infinitely continuous) or just a very good approximation of a (very fine) discrete system, which would naturally be expected to fail near a singularity.
Hopefully,
The 2nd law of thermodynamics is an aggregate description. It merely tells you what's likely or not. Fundamentally, everything is reversible, it's just that many timereversed processes require so finely tuned initial conditions we never observe them. The exception is black hole evaporation. According to Hawking's result, it's not reversible. Words and interpretations don't change anything about this. It's a result of a calculation, it's inconsistent, it a problem which requires a solution.
In Hawking's calculation there is no relation between the radiation and the ingoing state. That's exactly what I've explained in the above post. Sure, such a relation would solve the problem. That's solution attempt #1.
JimV,
I don't know what you mean by "in principle it could be." In usual quantum mechanics, it isn't. It's a reversible process. You can try to modify quantum mechanics to try to change that, yes. But modifying quantum mechanics is, if anything, even harder than modifying general relativity. Either way, you have to change something about the existing theories to resolve the disagreement. Best,
B.
How does the Born law relate to Information loss?
Even without black holes, it seems to me that information is lost due to Born's law.
A book burning is reversible (in principle). Does this mean there are no occurrences/applications of the Born law in a book burning, or that Born's law is reversible?
Or is this whole issue contingent on ignoring the Born law?
Is the horizon of BH the cause of the problem or just the start? What I mean is that once inside the horizon, every move closer to the horizon makes something inaccessible to something further out but still inside the horizon. Given this, it seems that to solve the paradox requires understanding the true nature of the singularity at the center.
Hi Bee, not a physicist here. Question about your statement "But modifying quantum mechanics is, if anything, even harder than modifying general relativity." Is the difficulty theoretical or experimental? In other words: is it difficult to conceive a mathematical modification that would fit existing data for QM, but cause reversibility to break down in regions of extreme curvature? Or is it one's natural reaction to the seemingly arbitrary nature of such a proposal? Or is it that such a theory, once conceived, would be impossible to test with current or nearfuture technology?
Jeff,
It is a point that is generally entirely underappreciated by laymen, that it is really hard to change anything about the existing theories so that the new theory is both internally consistent and consistent with all existing data.
There are some tricks that theoretical physicists have developed by help of which you can amend the present theories so that they still work and the new physics is safely hidden where it can't be observed (that's basically what my book is about). This works reasonably well for the standard model and the concordance model, but badly for general relativity and quantum theory itself. In these theories, even small changes can make a big difference and the whole thing breaks down  by which I mean it's either internally inconsistent or inconsistent with data, or both. Best,
B.
Jim,
What is Born's law? Do you mean Born's rule? It doesn't change anything about the problem, the inconsistency comes about already before measurement. You can try to argue, well, then why not just accept it because in the end we only measure probabilities anyway, so we can never prove a timeevolution was indeed unitary and so on. Yes, you can do that. Again, that amounts to modifying quantum mechanics, and you'd have to find a consistent way to do that  one that doesn't screw up the achievements of the theory. Many have tried, all have failed. Best,
B.
Michael,
The horizon isn't the problem. The horizon is merely the place beyond which information becomes inaccessible from the outside. It's the singularity that destroys the information and, eventually, results in the outgoing radiation missing information. (It turns from a pure state into a mixed state, in case you know the technical terms. Note however that even this pure state, could you preserve it, still wouldn't know anything about what formed the black hole.) Best,
B.
“Black holes emit radiation and this radiation doesn’t carry information”
It depends on the answer of the question: “What is information”. If theoretical phenomenological physicists have the conviction that information is something that can be transformed in an understandable way from configuration A to configuration B, the discrete radiation of a black hole carries information. Just because the sum of the radiation at any moment is bounded by the conservation of energy. So we know everything at any single moment we want to observe. We cannot say that there is no information, we have to say that we cannot understand the process of transformation. That’s quite a difference.
These kind of theoretical problems cannot be solved by theoretical phenomenological physicists who have no understanding of the foundations of physics and the corresponding foundations of mathematics. So yes, you are right. When it comes to the contributions of theoretical phenomenological physicists the black hole information paradox will outlive them all. Accept it.
Anyway, I liked your post.
Grimm,
"These kind of theoretical problems cannot be solved by theoretical phenomenological physicists who have no understanding of the foundations of physics and the corresponding foundations of mathematics. So yes, you are right. When it comes to the contributions of theoretical phenomenological physicists the black hole information paradox will outlive them all. Accept it."
Your condescending ad hominem attacks would be more successful if you'd do some background check prior to the attempt. It might have revealed I originally studied mathematics.
Having said that, your statement is plainly wrong. As I already explained above, the inconsistency does not depend on what exactly you mean by information. The referral to information is a red herring. If you had ever looked at the math, you would know that.
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