The first 17 minutes or so are a very well done, but also very basic introduction to the black hole information loss problem. If you’re familiar with that, you can skip to 17:25. If you know the BMS group and only want to hear about the conserved charges on the horizon, skip to 45:00. Go to 56:10 for the summary.

Last week, there furthermore was a paper on the arxiv with a very similar argument:

*BMS invariance and the membrane paradigm*, by Robert Penna from MIT, though this paper doesn’t directly address the information loss problem. One is lead to suspect that the author was working on the topic for a while, then heard about the idea put forward by Hawking and Perry and made sure to finish and upload his paper to the arxiv immediately... Towards the end of the paper the author also expresses concern, as I did earlier, that these degrees of freedom cannot possibly contain all the relevant information

*“This may be relevant for the information problem, as it forces the outgoing Hawking radiation to carry the same energy and momentum at every angle as the infalling state. This is usually not enough information to fully characterize an S-matrix state...”*

The third person involved in this work is Andrew Strominger, who has been very reserved on the whole media hype. Eryn Brown reports for Phys.org

(Did Hawking actually say that? Can someone point me to a source?)“Contacted via telephone Tuesday evening, Strominger said he felt confident that the information loss paradox was not irreconcilable. But he didn't think everything was settled just yet.

He had heard Hawking say there would be a paper by the end of September. It had been the first he'd learned of it, he laughed, though he said the group did have a draft.”

Meanwhile I’ve pushed this idea back and forth in my head and, lacking further information about what they hope to achieve with this approach, have tentatively come to the conclusion that it can’t solve the problem. The reason is the following.

The endstate of black hole collapse is known to be simple and characterized only by three “hairs” – the mass, charge, and angular momentum of the black hole. This means that all higher multipole moments – deviations of the initial mass configuration from perfect spherical symmetry – have to be radiated off during collapse. If you disregard actual emission of matter, it will be radiated off in gravitons. The angular momentum related to these multipole moments has to be conserved, and there has to be an energy flux related to the emission. In my reading the BMS group and its conserved charges tell you exactly that: the multipole moments can’t vanish, they have to go to infinity. Alternatively you can interpret this as the black hole not actually being hair-less, if you count all that’s happned in the dynamical evolution.

Having said that, I didn’t know the BMS group before, but I never doubted this to be the case, and I don’t think anybody doubted this. But this isn’t the problem. The problem that occurs during collapse exists already classically, and is not in the multipole moments – which we know can’t get lost – it’s in the density profile in the radial direction. Take the simplest example: one shell of mass

*M*, or two concentric shells of half the mass. The outside metric is identical. The inside metric vanishes behind the horizon. Where does the information about this distribution go if you let the shells collapse?

Now as Malcom said in his lecture, you can make a power-series expansion of the (Bondi) mass around the asymptotic value, and I’m pretty sure it contains the missing information about the density profile (which however already misses information of the quantum state). But this isn’t information you can measure locally, since you need an infinite amount of derivatives or infinite space to make your measurement respectively. And besides this, it’s not particularly insightful: If you have a metric that is analytic with an infinite convergence radius, you can expand it around any point and get back the metric in the whole space-time, including the radial profile. You don’t need any BMS group or conserved charges for that. (The example with the two shells is not analytical, it’s also pathological for various reasons.)

As an aside, that the real problem with the missing information in black hole collapse is in the radial direction and not in the angular direction is the main reason I never believed the strong interpretation of the Bekenstein-Hawking entropy. It seems to indicate that the entropy, which scales with the surface area, counts the states that are accessible from the outside and not all the states that black holes form from.

Feedback on this line of thought is welcome.

In summary, the Hawking-Perry argument makes perfect sense and it neatly fits together with all I know about black holes. But I don’t see how it gets one closer to solve the problem.

## 26 comments:

"One is lead to suspect that the author heard about the idea put forward by Hawking and Perry and then made sure to upload his paper to the arxiv immediately". that's a pretty nasty accusation to make without offering proof. (the same thing was said of Hilbert's publication of GR after hearing a lecture by Einstein). it would have been better to just not mention the paper at all.

I don't understand why you think that is nasty. I certainly would have done the same thing faced with the risk that my paper would get scooped.

Thinking that you probably misunderstood what I meant, I've rewritten this sentence. Better?

What Bee is guessing is absolutely standard and above-board behavior in mathematics. It's accounted for with the phrase "while we were writing up this work, we learned of the similar work..." There's really not a problem here.

Allen, I never said it's a problem. I just find it amusing since Hawking and Perry don't have a paper on the arxiv (yet).

I agree with you Bee.What Penna did was completely ethical and normal for a human being.When you have been working on a subject, being scooped by a well known scientist is far far worse than being scooped by a scientist of your stature!! That is a fact of life! In the latter case, no one will quote you! It happens lot of time.

> But this isn’t information you can measure locally, since you need an infinite amount of derivatives or infinite space to make your measurement respectively

You don't need an infinite amount of space to measure some number of BMS charges, up to some errors. Suppose you have a family of observers on some S^2 at large radius r. They may agree to each make certain local curvature measurements at an agreed-upon time, then bring the information back together (takes at least a light crossing time) and compare results. With a careful construction, they may measure the first several BMS charges—up to errors of some order in 1/r.

This takes finite space and finite time; and you only recover a finite amount of information, not all the charges.

Anyway, what's wrong with information being measured nonlocally? Isn't that to be expected if it's encoded nonlocally? I think we should relax about locality.

"

three “hairs” – the mass, charge, and angular momentum" and a buzz cut overall. A prism face totally internally reflects light (TIR; greater than critical angle contact at the glass to air impedance discontinuity). Discontinuity phase matching requires "forbidden" exponential decay per wavelength distance into the air (re Goos-Hänchen effect). Frustrated TIR is shallow sampling (solute IR evanescent wave absorbance in IR-opaque water).Black hole information leaks, access decaying quickly/distance from the external event horizon. If curvature causes default critical angle approach, information is trapped within the event horizon. (TIR phase shifts, Fresnel reflection coefficient being a complex number.) See? Easy!

"8^>)

Leo,

You misunderstood my comment. I wasn't referring to the BMS charges, I was referring to the information in the radial direction which, for all I can tell, is not in the BMS charges, unless you make an expansion in powers of 1/r. The higher the powers, the more space you need to measure the expansion coefficients (or the higher precision locally).

There is nothing whatsoever wrong with this! But the point that you can infer an analytic function in all of space by making a Taylor-series expansion around any point is hardly a new insight.

Funnily enough, I once wrote a paper pointing out that just requiring all functions, in particular the metric coefficients, to be analytic throughout space-time would remedy much of the information loss problem, though not all of it (it remains the problem how the quantum information gets into the *classical* metric - which indicates you really need quantum fluctuations in the metric to go ahead). I even had a name for this, I called it "strong holography," and was arguing that this is just a reflection of infinity not being realizable. But everybody who looked at the draft hated it, so I dumped it. They were probably right hating it.

Anyway, as you can easily tell, I've been going in circles through this paradox since 15 years or so... Best,

B.

Hi B,

I think we are actually talking about the same thing. The radial dependence is tightly tied to the angular dependence through the field equations which the metric has to satisfy. This is similar to the Newtonian case, where we know that the homogeneous solutions which are regular at infinity are of the form Y_{lm}/r^{l+1}. By measuring the part of the field with a particular l-pole structure, you are measuring something with a specific radial dependence. Back in the BMS group, the l=0 charge is simply the mass, the l=1 charge is the linear momentum, the l=2 charge is the generalization of angular momentum, and so on...

L

Leo,

What I am trying to say is that if you measure the l=0 charge and you get the mass, you do not know the density profile that you integrate over to get the mass. Best,

B.

In classical thermodynamics the invertibility is connected to the degradation of the mechanical energy into radiation; this degraded energy can not be reused to perform work. By cons, microscopically, it is always theoretically possible to reverse the process because the information on this process is not lost. This is a view of the mind because if "theoretically" it is not lost, "thermodynamically" it is lost. This is exactly the problem of the measure; the wave function is deterministic but any exact measure that would permit to reverse an irreversible process is not feasible.

The black hole is the reconciliation between the deterministic wave function and the indeterminacy of the measurement. Wanting to keep the wave function deterministic is absurd when, anyway, any measure of this wave function collapse in three numbers.

Aug 25, this blog reported: "I'm being told there will be an arxiv paper some time end of September probably." Could it be that's where Strominger "heard" it?

Emmette:

That's what I am trying to figure out. I keep reading "Hawking said" that there would be a paper. But for all I know he never said it, I was the one who said it. Unless I have missed something, thus my question.

Malcolm Perry resembles Dr. Okun in looks, a strange (not of this world) scientist in charge of research at Area 51 from the Independence Day :)

Yeah, not sure whether you owe a mea culpa, nor to whom… The Penna paper was uploaded Aug 26, more damning evidence ;)

Interesting Bee and thanks for helping to create perspective.

Supertranslations

Forget about black holes for the moment. Take a particle with nonzero spin. The fact that there's no gravity induced decoherence of the orientation of the spin indicates that the outgoing gravitational degrees of freedom don't encode the quantum information associated with the particle's spin orientation.

Now, take this spinning particle and throw it into a black hole. If the quantum information associated with its spin orientation were to come out encoded within the outgoing Hawking radiation, the mechanism for it can't possibly be due to encodings within outgoing directional gravitational charges at null infinity because they never encoded the particle's initial spin orientation in the first place.

“…the entropy, which scales with the surface area, counts the states that are accessible from the outside and not all the states that black holes form from”

However, in this case the first law of black hole thermodynamics in the form dM=TdS (M being the mass and T being the H. temperature) would be wrong.

Ivan: why do you think so?

I'm a bit confused about the source of concern in your classical shell example. In coordinates proper to exterior observers the shells of course do *not* disappear behind the horizon because the time coordinate of constant-radius observers becomes singular there. The outgoing information is exponentially redshifted. But information recovery is a matter of principle rather than practice.

From my understanding the problem is therefore inextricably quantum mechanical: information is lost in the map between the pre-singular star and the post-evaporation Hawking radiation field, not between successive Cauchy surfaces of the hole itself. Because one knows a certain amount of entropy must be evaporated per Page time the radiation field during collapse must also be modified, but this again arises from quantum mechanical considerations.

I agree it isn't obvious that sufficient information can be stored in the supertranslations as to actually do this. But I also don't see how the shell argument raises any special difficulty.

The other argument - that boson states need not uniquely specify a classical gravitational field - is more compelling. Certainly this is true if one achieves the coupling using the semiclassical Einstein equations. But this is somewhat adjacent to the information loss problem, which occurs even when the initial collapsing matter is classical dust (but a separate quantum field, decoupled from gravitation, lives in the spacetime giving rise to the Hawking effect).

Adam,

I don't know what you're trying to say. My example is supposed to illustrate that when you measure metric components (or gravitational radiation) at I^+ you don't get the full radial dependence. This has nothing to do with the formation of a horizon. That, I say, is the problem with the supertranslations. And it already exists on the classical level, without even speaking of horizons and such. (Incidentally, I kind of suspect that the charges, if you push them all the way to the horizon, vanish, so you better stay an epsilon away from it.)

As to the horizon, I agree to the extent that the horizon isn't the problem. What ultimately is the problem is the singularity. If you remove the singularity you already know information can't be destroyed. That in an by itself however doesn't explain how it comes out. Best,

B.

What is Stephen Hawking's most substantial idea of the previous, say, 25 years? Powdered mash has more words in its ingredients than his articulation, non-trivial meaning of which no-one ever seems clear.

He did some good work as a young man, and sadly succumbed to an untreatable degenerative disease. His wife wrote him a successful though not very good popular science book. Some of the financial windfall he spent on very publically divorcing her, he humiliated her.

Anyway it wasn't a memorable book. That was about 1990. Hawking radiation was a good idea but a relativity or mechanics it was not. The stain of his book after that, and since then, precisely what?

Sabine, may be I didn’t quite catch what you said but I had in view the following.

The entropy of a black hole is much lager than that of a collapsing body (together with all the higher multipole moments radiated away during collapse).

The concept of the entropy of a system has a physical meaning only if the system is in complete statistical equilibrium. An arbitrary black hole, like a thermodynamic system, reaches an equilibrium (stationary) state after the relaxation processes are completed and all the higher multipole moments are radiated away. In this state, it is completely described by fixing a small number of parameters, e.g. M, J, Q.

If we regard the mass of a black hole M as the total internal energy of the black hole and the Hawking temperature as the temperature of the black hole T, then the Bekenstein-Hawking entropy must be the total entropy of the black hole in accord with the first law of black hole thermodynamics dM=TdS.

Ivan,

Indeed, I think you didn't quite catch what I said. There is no reason why the entropy that appears in this equation should contain information about states that are causally disconnected. Consequently arises the question why S should count all the information in the volume, including those with which you cannot interact ("strong interpretation of the BH entropy"), or if it not instead counts only the information which is accessible from the outside ("weak interpretation of the BH entropy"). This isn't a question you can answer just by alluding to the thermodynamic analogy, you'd really have to know what happens to the degrees of freedom/black hole microstates.

This discussion is almost as old as the black hole information loss problem. Not that I have actual survey data, but I think most physicist opt for the strong interpretation. I don't, that's what I'm saying. Best,

B.

Having read Penna's paper, I have an idea about this. He mentions that in order to resolve infinities with the BMS charges on the horizon work, you need to take the limit as the stretched horizon. That gives a couple of energy scales: the temperature of the Hawking radiation at the stretched horizon and the energy corresponding to a wavelength equal to the distance between the stretched horizon and the real horizon.

I think that to calculate the BRS charges, as you take the limit of the stretched horizon moving towards the real horizon you need to use the effective field theory appropriate to one of those energy scales. So initially you only need to include gravitational waves and electromagnetic waves, but as that energy scale passes the quark deconfinement energy the SU(3) of gluons becomes relevant, which will add more BRS charges. Similarly as it paasses the electroweak unification energy, the U(1) for photons turns into the U(1) x SU(2) of the electroweak force. (I'm not sure what happens when the energy scale passes the neutrino/electron/muon etc res masses). So the limiting process includes renormalization flow and so forth.

We don't yet know the physics above the Standard Model scale, but all the candidates I can think of will also affect this limiting process: GUT unification would be like other reunification gauge symetry breaking, supersymmetry would presumable turn BRS charges into supercharges (via super-supertranslations :-) ), and compactification would become relevant around the compactification scale where the horizon surface turns from S^2 into S^2 x the compactification manifold.

Figuring out the details of this would be a very interesting filed theory calculation (and likely a great way to study holography). But one can see how there would be a hope that the density of BRS charges at each energy scale was related to the field content of the effective field theory at that scale, giving a possibility that the process could yield just the right number of charges to ensure a consistent quantum mechanics with no violation of unitarity. It might even put some interesting new constraints of viable field theories.

One can also see how this limiting process could stop at the Bekenstein-Hawking entropy (as it does in the string fuzzball calculation and, up to the Imirizi parameter, in Loop Quantum Gravity): due to quantum fluctuations in the metric, the posision of the event horizon is only defined to within the Planck length, and BRS charges separated by less than of the order of the Planck length cannot be distingushed. So you get a limiting entropy that scales as the area of the horizon in Plank units.

Post a Comment