Update: Jacques Distler criticizes this paper. His maiden of all complaint is a refined version of an objection I wrote below. Strominger, Hawking, Perry redefine the rules of the game too claim that the BMS symmetry transformations at the horizon aren't redundancies (like gauge symmetries inward the mass should be) but existent symmetries, so states don't receive got to hold out invariant nether them too 1 may hit novel states. Jacques also believes that a sure diagonal BMS subgroup is ill-defined for an evaporating dark hole. Finally, Distler agrees amongst my primary full general dot as good – Hawking et al. locomote within local acre theory where the information loss paradox was born too may hold out shown to hold out trouble. Some nonlocal twist is needed to avoid the paradoxes. Jacques insightfully says that local quantum acre theory breaks downwards non alone locally at brusk distances. It has to interruption at the really long Page fourth dimension (when the dark hole has reduced its entropy to 1/2) because at that time, the entanglement betwixt the early on too tardily Hawking radiations must start to demonstrate up.This is a continuation of the storey most the BMS supertranslations too their relevance for the dark hole mysteries.
Gross, Hawking, Witten, Strominger, Yau. Note how similar the photograph is to these images of 5+ supersymmetric heroes from dissimilar movies.
Andy Strominger was just interviewed yesteryear a author for Scientific American – non precisely 1 of the journals nosotros silent respect, to pose it mildly (if I receive got to avoid the term "greasy šit") – most his recent locomote most soft hair:
Stephen Hawking's New Black-Hole Paper, Translated: An Interview amongst Co-Author Andrew StromingerWell, this championship is bizarre – it's a newspaper yesteryear 3 authors too non just Stephen Hawking's too Strominger is inward no way a "junior" co-author. One could inward fact say that Strominger is the leader of this sub-industry too Hawking along amongst his one-time co-author from 1978 too 1983 Perry receive got decided to hold out Strominger's grad students for a piece again.
(However, 1 must sympathise that SciAm doesn't write for people who receive got a clue. It writes for SciAm commenters over in that location similar "essentia" who alone asks "what form of scam is this?" too "naro10" who alone says that Hawking has allegedly blamed the State of State of Israel for the existence of the dark holes LOL. This is non what the interview is about, "naro10"! The remaining 2 commenters offering mushed potatoes involving negative entropy too fractals; too the claim that dark holes are just neutron stars. Swines bombarded yesteryear pearls.)
But the interview is fun too Andy says lots of things nicely. Why the information loss looks terrible to the physicists (well, the word "determinism" looks also old-fashioned for the unitarity inward quantum mechanics given the powerfulness of QM to predict probabilities alone but 1 implicitly hopes that Andy isn't fundamentally misunderstanding something similar that) but why it has seemed truthful at some point, anyway, why yous can't escape from a dark hole (because the horizon is a sphere expanding outward yesteryear the speed of low-cal whose surface area just happens to hold out kept fixed thank yous to the spacetime curvature), what the Strominger-Vafa derivation has changed, too so on.
Be sure that I handle amongst some 90% of what Strominger said inward the text as a whole.
And I also handle amongst some mathematical claims most the BMS symmetries, Andy's claims that some of these observations he too pals made are interesting, too most the thought that it should hold out useful to written report them closer too investigate their touching on the dark hole mysteries too that they receive got isolated a distich of these interesting games that should learn us something. However, I disagree amongst the proposition that the dark hole entropy has been shown to hold out (partially or completely) carried inward the shape of the "soft hair" located at the trial horizon.
There are several other sentences that heighten my eyebrows, however, such as:
And when its unloosen energy is zero, there’s a feel inward which yous tin recollect of it as living on the boundary of spacetime.By the Fourier transform, depression unloosen energy is linked to depression frequencies too hence long times – which is ordinarily correlated amongst long distances. But within AdS/CFT too in all probability other consistent descriptions of the quantum information, if 1 talks most the locus close the boundary of the spacetime, I recollect that most people would handle that it is associated amongst the high-energy (ultraviolet, UV) degrees of liberty inward the theory (CFT), non the low-energy ones! On the contrary, the low-energy CFT degrees of liberty "live" close the centre of the AdS.
But dorsum to the novel message of the text.
Andy has already interpreted the one-time BMS supertranslations – some diffeomorphisms that human activity inward a elementary way on the asymptotic scattering part at infinity so that 1 gets "a parameter" for the transformation for each dot on the sphere \(S^2\) – as a root of some novel excitations too degrees of freedom, soft photons too gravitons of some form which are associated amongst the horizon for some reasons.
With Hawking too Perry, they struggle that these soft photons are excited whenever a charged particle falls to the dark hole, too depending on how it does that, the dark hole becomes "different". Similarly, soft gravitons should hold out added to the horizon whenever a particle amongst the energy-momentum crosses the horizon, too this soft graviton – a ingredient of the soft pilus – modifies the microscopic setup of the dark hole. The soft pilus ultimately influences what the dark hole precisely emits as good too they claim to know something most the dependence.
Strominger is happy that the part where they house some "special novel stuff" is the trial horizon so it has the surface area of the trial horizon too 1 could acquire the right entropy. Except that they can't acquire the coefficient \(1/4\) inward this case. He suggests that it is non a large defect.
I recollect that Andy isn't also familiar amongst the non-stringy literature claiming to explicate the dark hole entropy. We used to handle that those papers were garbage but I recollect that he couldn't receive got known what nosotros were precisely talking most because, yous know, the primary message of this novel newspaper isn't "radically" dissimilar from the totally idiotic claims e.g. inward loop quantum gravity that they tin calculate the dark hole entropy (also without the right numerical coefficient) yesteryear surgically removing the interior too adding some special Chern-Simons stuff at the horizon etc. But in that location are tons of sloppy papers "calculating" the dark hole entropy without the numerical coefficient. Almost all of them are garbage too all the remaining ones are using a mathematically uncontrollable formalism.
You know, if yous know the right result, \(S=A/4G\), it's really slowly to fool yourself into thinking that "the information must hold out carried yesteryear something at the trial horizon", so 1 invents some exception for the horizon, claims that the typical length scale is the Planck scale, too the happy destination follows, \(S\sim A/G\).
The Bekenstein painting amongst qubits inward a higher house is a typical illustration of that way of thinking. Qubits – quantum degrees of liberty described yesteryear 2-dimensional Hilbert spaces – are placed all over the horizon. And that's how the dark hole "works". The painting is a dainty 1 optimized for pretty pop talks but my discussions amongst Bekenstein made it clear that he had genuinely believed this form of discreteness. So he genuinely believed inward the heavily discrete spectrum of areas – integer multiples of \(4G \ln 2\). If this discrete spectrum were translated to a discrete spectrum of mass/energy, dark holes amongst such a heavily discrete unloosen energy spectrum would receive got no take chances to emit anything similar a thermal radiations because the unloosen energy of the quanta would basically receive got to hold out integer multiples of the Hawking temperature or so.
You may hold out happy that the Bekenstein "model" of the dark hole on the painting reproduces the right entropy if yous pick out the triangles' areas to hold out \(4G\ln 2\), an unnatural value (which was why Bekenstein, similar the loop quantum gravity crackpots, got so excited most my too so my+Neitzke newspaper most the quasinormal modes). But if a model may reproduce 1 slice of data, it doesn't hateful that it's the right model. One understanding isn't plenty to seek a hypothesis; but 1 disagreement is plenty to disprove it. The painting inward a higher house is genuinely wrong for many reasons.
First, as I said, the spectrum of the horizon areas etc. only cannot hold out discrete, at to the lowest degree non amongst this huge spacing. Second, the information inward Nature is almost never encoded inward qubits. Qubits are man-made concepts that are helpful for computers but natural systems only don't locomote similar that. They send the information inward much to a greater extent than full general degrees of freedom. H5N1 highly excited nation inward 2D conformal acre theory carries the information inward the inquiry "which microstate at the given flat nosotros pick". H5N1 given excited flat of a CFT isn't a tensor production of many qubits; the degeneracy is almost never a powerfulness of two. The degeneracy may alone roughly computed from Cardy's formula too Cardy's formula has an exponential shape – but the natural base of operations of the exponent is \(e\), non \(2\), of course. Nature stores the information inward nats, non bits. That's why nosotros utilization the term "natural logarithm" for the base-\(e\), non base-2, logarithm.
So this painting involving quantum binary digits is just naive – partly inspired yesteryear people who may receive got listened to the mutual estimator architecture much to a greater extent than than to Nature. But a to a greater extent than serious employment is that the thought that the information is carried strictly yesteryear some "new construction at the horizon", some Planckian vicinity of the strict trial horizon, is wrong, too. I am sure that many people believe it in 1 trial they larn most the \(S=A/4G\) formula too maybe I believed it years ago, too. But in that location only cannot hold out whatsoever special construction that "must" hold out placed on the trial horizon too nowhere else.
As I previously argued, the location of the trial horizon is alone known inward the futurity in 1 trial yous know the whole spacetime geometry. The trial horizon is a spherical trounce around the stellar centre expanding yesteryear the speed of light, as Andy also said. But when the dark hole (and its trial horizon) begins to form, it starts at a seemingly random 2nd when the centre of the star becomes the "first" dot that belongs to the trial horizon. It's followed yesteryear tiny too so larger spheres around the stellar center. There is silent no singularity there. At some moment, the growing sphere devours the surface of the star too the dark hole is basically "complete". The curved shape of the spacetime is so huge that fifty-fifty though the sphere keeps on expanding along a null surface, the surface area of the sphere stops growing. When the oscillations acquire stabilized a niggling bit, yous acquire a nearly static dark hole spacetime and, if yous were lucky to receive got picked the initial dot of the trial horizon correctly, yous may run into that the the interior side of the trial horizon indeed contains all the points from which yous can't escape to infinity (to the dark hole exterior).
But if something were changed most the futurity development of the collapsing star (some novel star would locomote far to speed upwards or wearisome downwards the formation of the dark hole), the locus of the horizon could hold out elsewhere, or it could start to grow before or later. There exists no "local condition" yesteryear which yous could seat the house of the trial horizon around yous at a given moment. To discovery the seat of the trial horizon around yous genuinely way to brand a successful prediction of the distant future.
That is why it is completely wrong to imagine that something materially dissimilar is taking house (or some objects or degrees of liberty are located) at the horizon "in existent time" although they can't hold out located anywhere else. Such a claim is wrong for a elementary ground – the laws of physics that would imply such special "objects" at the trial horizon would hold out acausal. They would know something most the development of the spacetime inward the distant future. They would receive got to know it, otherwise they couldn't know where the "new horizon-bound objects" should hold out supplemented.
So the trial horizon may alone play a purpose inward the laws of physics if yous depict this physics from the viewpoint of an observer who ultimately knows most the whole future. Clearly, it must hold out an exterior observer who didn't autumn into the dark hole. But because he didn't, he doesn't run into into the dark hole, either. For him, the horizon is the boundary separating the accessible business office of the basis from the inaccessible one.
Now, in that location is some feel inward which the horizon must shop all the information etc. from the viewpoint of the exterior observer. For the exterior observer, the dark hole is covered yesteryear a conducting warm membrane etc. too aught beyond the membrane (beneath the horizon) exists; it's the membrane paradigm. In which shape this information is stored? AdS/CFT has an answer. In AdS/CFT, the CFT genuinely doesn't easily run into within the dark holes. Some extra locomote is needed to figure out what's happening inward the interior too people doing that (like Papadodimas too Raju) aren't quite sure whether the reply has to hold out unique. But what nosotros practise know is inward what shape the CFT encodes the information stored inward the dark hole: the microstate is just some random near-thermal microstate composed of the gluons or whatever the CFT contains.
But within the CFT, it is really difficult to say "where" objects are inward the AdS bulk. The locality inward the bulk, peculiarly when it comes to the precise localization of objects too events according to the novel radial (holographic) direction, is an extremely tough business. I am confident that almost all AdS/CFT folks who receive got also studied the dark hole information puzzles volition handle amongst me that the information described yesteryear the "thermal nation of the CFT" isn't inward whatsoever canonical way localized strictly at the trial horizon of the dark hole. It's to a greater extent than sensible to say that it's localized "almost anywhere". If yous alter the thermal nation of the CFT yesteryear 1 particle, this particle may hold out reconstructed to hold out nearly anywhere inward the bulk, sure as shooting at distances comparable to the dark hole radius from the trial horizon (but outside).
So I recollect that the thought that the degrees of liberty of the dark hole "should" hold out located strictly at the trial horizon doesn't genuinely follow from whatsoever of the BMS derivations too whatsoever of the novel (or resuscitated) legitimate GR stuff that these papers yesteryear Strominger too pals receive got covered. Instead, this thought of an "exceptional construction at the trial horizon", the "soft hair", comes from the one-time wishing to explicate the Bekenstein-Hawking entropy inward an slowly way. But this slowly explanation is acausal. And every bit importantly, it is indefensible from the viewpoint of an infalling observer. Once nosotros encompass the infalling observer's perspective too take the existence of the dark hole interior, in that location only cannot hold out anything special whatsoever most the location of the horizon. The trial horizon isn't a metallic element (or glass) trounce inward whatsoever sense. There's aught to proceed yous there. If yous acquire also unopen to the horizon (so that your rocket jets only can't receive got plenty unloosen energy to salve you), you're basically guaranteed to hold out sucked in.
In 4D etc., the no-hair theorem is genuinely true. (Fuzzballs as good as dark holes of assorted topologies may hold out said to hold out counterexamples inward higher spacetime dimensions.) One may seek to engineer a philosophy inward which the no-hair theorem is wrong because of some "fine Planckian stuff" too Hawking-Perry-Strominger are in all probability an illustration but I recollect that this whole sweat to invalidate the no-hair theorem inward 4D is just misguided.
While the BMS-related GR equations inward these papers are in all probability right, I recollect that the ways how they connect them amongst the dark hole information too quantum gravity are ultimately deeply flawed. If some degrees of liberty are assigned strictly to the trial horizon, it should hold out just a detail choice of a "gauge", 1 of many methods to integrate the interior out, too so on. One can't imagine that something special is "really" happening at the trial horizon.
Andy seems to recollect that these claims most the information's existence carried yesteryear the soft pilus receive got been "derived". I suspect that the employment is that he isn't interpreting the status of the BMS transformations correctly. He views them as global symmetries that are capable of producing novel physical states. The BMS transformations nontrivially human activity at points at infinity – similar the stiff translations of the Minkowski or AdS infinite – so they powerfulness await similar global transformations.
Still, they are diffeomorphisms too they seem to depend on also many parameters – similar the generic diffeomorphisms acting purely inward the bulk. The latter are gauge symmetries so all physical states receive got to hold out invariant nether them. Their generators (at to the lowest degree if they human activity trivially at infinity) receive got to annihilate the physical states. I suspect that this volition partly hold out truthful for the BMS supertranslations, too. H5N1 part, many, most, or all of the states that they consider physical, distinguishable, too nonzero volition hold out unphysical, indistinguishable, or zero.
When Strominger says
And so in that location are infinitely many vacua, which tin hold out thought of as existence dissimilar from 1 some other yesteryear the add-on of soft photons or soft gravitons.you should run into an obvious tin of worms, I think. For a given Minkowskian or AdS compactification, the vacuum nation is unique. You may utilization a formalism inward which the nation is multiplied too many gauge copies etc. are created but at the end, yous shouldn't forget that this degeneracy was a line a fast 1 on too yous must take the clones (like inward the green gauge symmetry). It seems to me that they're at to the lowest degree partly failing to practise this business office of the locomote so many of their "new states" are unphysical bogus.
I don't know the precise rules but I recollect that the right qualitative description of the status of the BMS supertranslations too the novel "soft hair" states volition resemble e.g. the recent locomote on the intercontinental Wilson lines. In that paper, the operators would hold out trivial or equivalent if they alone acted on 1 of the AdS boundaries but 1 tin define a "comparison" betwixt 2 AdS boundaries too that's where novel operators (like the Wilson lines) may arise. Note that inward that paper, the operators are "nonlocal", associated amongst lines going through the whole spacetime. I believe that when the qualitative naive conceptual mistakes are fixed inward the Strominger-Perry-Hawking setup, they volition receive got a similar picture. Nothing volition "force us" to recollect that some novel degrees of liberty are located precisely at the horizon. It volition hold out at most 1 "gauge", a parameterization to depict the conduct of Wilson lines or similar nonlocal or "comparative" objects.
There are several other angles from which I await at their claims too that await seriously wrong to me. The really claim that the information should depend on some sparse "Planckian shells of exceptional behavior" seems to locomote against the results of many years of recent QG enquiry – peculiarly the entanglement-glue duality.
I recollect that 1 of the broader lessons nosotros receive got learned is that
whenever nosotros depict physics too the information inward damage of the bulk, nosotros are allowed to assume that the local spacetime geometry is perfectly smooth.So in that location is never whatsoever "need" to imagine that nosotros must hold out careful most shapes at a better-than-Planckian accuracy. The ER=EPR correspondence – which I sentiment as a special subclass of solutions to the Papadodimas-Raju constraints – goes farther too says that if yous depict the information carried yesteryear 2 similar dark holes, yous receive got at to the lowest degree 2 polish geometries yous tin use. You may either assume that the dark holes are separate; or they are connected via an Einstein-Rosen bridge.
Note that the smoothness comment inward a higher house doesn't say that the metric tensor cannot fluctuate. But the fluctuations may ever hold out viewed as extra excitations added on elevation of a perfectly polish spacetime too these excitations are basically composed of gravitons whose reveal is finite or small-scale for low-energy states.
The dot of my comment most ER=EPR is that these are 2 polish spacetime geometry that "dramatically", topologically differ. But both of them are silent perfectly fine. Consistent quantum theories of gravity never strength yous to imagine that the precise shape of the spacetime has some complicated Planckian or sub-Planckian wiggles yous must carefully adjust. There are no wiggles. You may too yous should allow the background spacetime to hold out any reasonable plenty polish geometry (perhaps 1 obeying some classical/effective equations) too if your theory of quantum gravity is consistent, it volition allow yous to depict the degrees of liberty inward damage of objects or fields on elevation of this polish geometry.
To say that some Planckian or sub-Planckian accuracy is needed to recover physical information most the microstates seems to contradict the most successful lessons from the recent decade or 2 of QG research. Well, fuzzballs practise wishing to depict dark hole microstates inward damage of some fine solution but at to the lowest degree these are solutions inward the whole dark hole interior, keeping a polish spacetime amongst no preferred measure-zero loci.
Strominger, Hawking, too Perry envision some potential of the total quantum theory of gravity to shop a huge amount of information inward some book – the trounce close the horizon. But why couldn't similar degrees of liberty hold out "everywhere"? Don't yous predict, just similar the qualitatively analogous (as I mentioned) loop quantum gravity papers, that in that location should hold out a volume-extensive entropy of the dark hole, too perchance an infinite entropy?
H5N1 paragraph indicates that Strominger is totally aware of the employment but he sweeps it nether the rug:
One matter that bothered us most this right from the really offset is: Why doesn’t this allow an infinite amount of information? We don’t wishing an infinite amount of information. Ultimately we’d similar to somehow utilization this to recover the Hawking-Bekenstein surface area entropy law. It looked similar nosotros were getting an infinite amount of pilus because yous seem to hold out able to receive got these soft photons that had an angular localization that was arbitrarily small. But there’s no physical way to excite 1 of those. So those are non physically realizable states of the dark hole.Yes, he says, they seem to predict an infinite amount of bogus information that may hold out carried yesteryear that type of soft hair. But except for a finite subset, Strominger wants to believe, these degrees of liberty cannot hold out excited. It silent doesn't explicate why in that location are non tons of these novel degrees of liberty associated amongst other null surfaces that also receive got the potential to hold out identified as trial horizons inward the future. And he doesn't explicate why they cannot hold out excited – for what reasons their classical description breaks down. But these are non the biggest problems here.
The biggest employment is that the alone way how quantum gravity may protect us against this invalid proliferation of states (and from volume-extensive entropy) is really dissimilar too requires some UV/IR mixing too hence nonlocality. Why can't nosotros probe sub-Planckian distances? Because when nosotros accelerate the future-LHC protons at the trans-Planckian energies, their collisions start to hit dark holes that are ever larger. The recipe to "shorten the distances yesteryear increasing the energies" breaks downwards because at some dot (the Planck unloosen energy – but inward string theory, it may hold out inward some feel earlier), the intermediate states visually grow bigger so they involve some nonlocal conduct (and thermalization) of an object that is extended to distances larger than the Planck length too increasing.
It's really of import that nosotros say that some novel QG/stringy physics breaks the QFT recipe "higher energies way shorter distances". But this recipe is a QFT recipe as I said – it straight follows from the painting of local fields. String theory (or whatsoever consistent theory of quantum gravity if in that location were some other one) tin alone truncate the hunt for ever higher energies (it truncates it at the string or Planck scale) yesteryear not existence quite local. The information tin alone locomote out of the dark hole yesteryear a nonlocal process. You tin utilization local effective acre theories as long as no dark holes appear etc. But for dark holes, peculiarly in 1 trial they grow bigger, the overwhelming business office of the information that the dark holes send must hold out stored inward "nonlocal" degrees of freedom. To say that they should final result from local degrees of liberty inward the normal spacetime would hateful to claim that a local description is valid fifty-fifty inward the presence of the dark hole – too that would take us dorsum all the bogus volume-intensive degrees of liberty etc.
And Papadodimas-Raju receive got reformulated the employment of co-existence of the dark hole microstates too the local fields as an inverse employment to reconstruct (the algebra of) the fields that may hold out defined on a given Hilbert infinite of microstates. This is a complicated inverse employment because the whole algebra of the fields must obey some given conditions. In this way, Papadodimas-Raju genuinely run into that the spacetime is emergent. It's emergent because the acre operators are alone a possible extra construction added on a Hilbert infinite – a construction (solution) that isn't guaranteed to exist; but a construction (solution) that may also hold out non-unique. T-dualities, U-dualities, string-string duality, AdS/CFT, too ER-EPR correspondences acknowledge 2 or to a greater extent than seemingly dissimilar spacetimes whose physics is equivalent. This only way that in that location are many solutions (in a sure category obeying some weather condition such as the "shared" Hamiltonian) to roughly or precisely define all the acre operators on a sure Hilbert space.
It seems to me that Hawking, Perry, too Strominger are working within the conceptual framework inward which everything, including the dark hole microstates, must hold out constructed out of some (quantized) local fields, basically a straightforwardly quantized GR. They wishing to believe it's possible after all because they receive got rediscovered a previously understudied too potentially underestimated characteristic of classical GR, the BMS supertranslations too similar objects, too they wishing to believe that this novel add-on may hold out plenty to brand the innately local description of quantum gravity possible. Within this intrinsically local framework, it's ever possible to say "where" the information resides, too they have to claim that the dark hole entropy is genuinely stored at the horizon. One may confidently say that if the Hawking, Perry, Strominger painting were right, the spacetime wouldn't hold out emergent at all.
Nevertheless, I recollect that this painting of the old-fashioned, non-emergent spacetime – which many non-experts believe as good – represents an sweat to provide physics yesteryear decades, perchance before the holographic principle, too it has been debunked too superseded yesteryear a novel image that makes much to a greater extent than sense. And I am confident that most experts inward the dark hole information line of piece of work organization genuinely handle amongst my full general criticism.