Guest Post: Black Holes, Quantum Information and Fuzzballs

Today's guest post is by Weizmann Institute physicist, Prof. Micha Berkooz. Berkooz, a string theorist, recently organized a conference at the Institute on "Black Holes and Quantum Information Theory." We asked him about Hawking's recent proposal, reported in Nature under the headline:"There are no black holes."


Celebrated theoretical physicist Stephen Hawking has opened a can of worms in his 1976 paper on black holes. In a recent article, he is trying to put the worms back into the can. It may prove a little trickier than expected.

Black holes are solutions of Einstein's equations of general relativity which have the unique property that they posses a closed surface in space which is the ultimate "point of no return." Even the fastest things that nature allows us - light rays - will not escape if they cross this surface, dubbed the horizon. Despite their strange properties, black holes are not really exotic objects. In the theoretical realm, if one takes enough matter, throws it all to a point and fast forwards using Einstein's equations, one ends up with a black hole. In the observational realm, there is ample astrophysical evidence that massive stars end their life as black holes, and that there are mega black holes at the center of many galaxies (including our own).


But black holes don't just gobble things up. Rather they quite effortlessly chew things up - thoroughly and completely - and spit them out in a completely indecipherable form. This is the main point of Hawking's work from 1976, in which he showed that a black hole in empty space emits precisely thermal (black body) radiation when quantum mechanics is taken into account. In fact it emits thermal radiation until it completely evaporates, and any initial state of the system will end up exactly the same, in the form of thermal radiation.

Very loosely we can understand this as follows: Consider creating an electron and positron pair, in a specific quantum state, just outside the horizon. Each of these particles can have either spin up or spin down so there are a total of 4 states. Suppose the black hole now gobbles up the positron, never to be seen again, and that the electron makes it back to our lab. The electron has only two states. So we started with a system which had 4 states and ended with a system that has two states - we lost information! Equivalently we can say that quantum mechanics is not unitary (reversible) in the presence of black holes, or in more technical terms we can say that the emitted electron is in a density matrix and not a pure state, just the same as exactly thermal radiation.

Hawking's computation is extremely elegant and robust - it only uses 1) quantum field theory on 2) curved space. The former is well tested and verified in just about any high energy physics experiment, and the latter is just Einstein's general relativity (as a classical theory). Furthermore, a very similar set of computations is successful in the context of generating the structures in the universe from primordial quantum fluctuations after the big bang. Yet around the black hole, the synthesis of these two sets of ideas leads to a bewildering result, since any high-enough energy experiment will create a black hole, and end in information-free thermal radiation. The universe just can't help losing the information of where the keys are. This is unlike any other quantum mechanical system whose time evolution does not lose any information.

Interestingly, the surprising prediction for a flux of thermal radiation from a black hole fits very nicely with other properties of the black hole. Shortly before Hawking's article, Jacob Bekenstein suggested that black holes have entropy. Bekenstein's entropy, Hawking's temperature and the mass of the black hole, which is the same as its energy, satisfy the ordinary laws of thermodynamics.

The synthesis of quantum mechanics and general relativity has been an outstanding problem for quite some time. Using string theory, and more specifically Maldacena's AdS/CFT correspondence, it was finally established that evolution of black holes is unitary and that we do not lose any information, since we can embed black holes in standard quantum theories which we know are completely unitary. In these theories, black holes seem no different than lumps of coal that burn. The issue remains, however: Where exactly does the synthesis of field theory and classical general relativity fail, and which of their well tested properties are we forced to modify?

There has been a renewed interest in this question in recent years. An elegant argument from Almheiri, Marolf, Polchinski and Sully suggested that one needs to quantum-mechanically modify the horizon of a black hole into a hot membrane (whose nature is not clear). This solution has been called the "firewall" solution. In this solution, one gives up some aspects of Einstein's equivalence principle, as well as parts of the black hole solution in classical general relativity, where it naively seems that quantum effects should be small.

In another solution, suggested a few years ago by Mathur, one replaces the black hole by a large set of horizon-free solutions of string theory - this is the "fuzzball" solution. This solution is quite attractive, but so far no one has been able to construct enough "fuzzballs" to account for the black hole entropy. Other solutions suggest some non-locality in space-time, which allows information to be transported from the interior of the black hole to its exterior, or replacing space-time itself by an algebraic construction, keeping only quantum mechanics. Hawking conceded already 10 years ago that black holes do not really lose information, and his recent paper provides evidence for the "fuzzball" proposal for the description of black holes.

This topic is one of the topics of research of the String theory group at the Weizmann Institute, Profs. Ofer Aharony, Micha Berkooz, Zohar Komargodski and Adam Schwimmer, who hosted a workshop on "Black Holes and Quantum Information" earlier this month. The workshop explored the role of entanglement entropy and quantum information theory in the resolution of the black hole information paradox, and in the very emergence of space-time as a derived concept, which seems to appear in a way similar to how thermodynamics is derived from statistical physics.

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I think you mean indecipherable. Although close terminology, Un-decipherable refers specifically to speech and writing and asserting an impossibly of ever deciphering. Whereas, in-deciperable is a more general term suggesting a still present potential for decoding. Scientific method would suggest more patience than denial, with data that is. I could be wrong but that is science.

By Charles Alexad… (not verified) on 29 Jan 2014 #permalink


By Charles Alexan… (not verified) on 29 Jan 2014 #permalink

thanks. Any editing slips are mine. WSW

And at what point in time would the information have been lost to the universe in Hawking's original synthesis? There's something wrong right there.

By Tom Cohoe (not verified) on 29 Jan 2014 #permalink

I believe that these black holes are the subconscious of all things...and inside of them is the dream state always and I mean always preparing its self for the conscious state which is where we are now...they are a blend of life asleep and life past on...

By Orlando Carlo II (not verified) on 31 Jan 2014 #permalink

In layman's terms, what comes across (by analogy, therefore very likely wrong) is the idea that the event horizon of a black hole isn't a hard boundary like a shell, but rather a gradient or gradual boundary, like the atmosphere around a planet that gets more dense as one gets closer to the planet's surface. At the boundary's furthest extent from the singularity, it sucks in objects with larger mass; and at some point much closer to the singularity, it sucks in photons.

I read the linked article about information paradox.

It seems to me that a mechanism involving nonlocality would fulfill a number of criteria.

Information wouldn't be "lost," it would exit the black hole in a form that "would be" decipherable (in the cryptanalytic sense) "if" the outside observer also had the corresponding information from inside the event horizon. The entire system conserves information ("inside" plus "outside"), but a local observer either "inside" or "outside" only has half of what they need to render their observed bit stream into actual information rather than apparent noise.

If we assume that nonlocal interactions are truly instantaneous, as in, "infinite velocity", then by definition that velocity overcomes the attraction of the singularity: the "information" (in "encrypted" form) escapes.

Lastly a question re. gravity as a "consequence of thermodynamics": what's the mechanism? How does thermodynamics produce gravity, other than the obvious that successive stellar life cycles are entropic, and stars (and the planets accreted around them) exhibit gravity?

Since gravity causes objects to clump together and stick, one could speculate that gravity is the meeting-point or intersection between dissipation (entropy) and accretion (negentropy).

OK, feel free to tell me where I thoroughly screwed up on this. At the purely conceptual level it seems to make sense, but that means nothing until there's math to support or falsify it.

Here is what I meant in #4. General relativity says that all coordinate reference frames are equally valid. In some of them, it takes infinite time for something to reach the horizon. It is why black holes used to be called 'frozen stars'. If it can be said at any finite coordinate time T_0 " that "information has now fallen through the horizon" that amounts to invalidating all the coordinate reference frames in which the particle would fall through the horizon at a time later than T_0, which is a contradiction of general relativity. For anything to fall through the horizon, or for a horizon to even form in coordinate time is a violation of general relativity.

By Tom Cohoe (not verified) on 01 Feb 2014 #permalink