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#11




Paradox unexplained
On 4/3/2016 11:32 PM, Steven Carlip wrote:
On 4/1/16 4:47 PM, Jos Bergervoet wrote: For the black hole information paradox I would expect two seemingly conflicting results (as is necessary for a paradox by definition,) e.g. like: 1) We know that information is lost because [...] We believe that matter in a pure quantum state can collapse to form a black hole. This is not quite clear if we cannot provide the solution of the GR equations that show the formation (so indeed we now can only say that we "believe" it). In particular, the often shown KruskalSzekeres diagram like this one he http://i.stack.imgur.com/U2EFS.gif is certainly *not* the correct description of formation, temporary existence and final complete evaporation! What it may describe correctly is an eternally existing black hole evaporating at the same rate as accreting new mass (in homogeneous form, GW150914 is not a good example!) Any mass in Region II (positive V axis) would never come out and would not contribute to any paradox in this case. The mass falling in would linger very long (in Schwarzschild time) above the horizon and would obviously have ample time to imprint its information on the Hawking radiation being emitted there. In fact the infalling information is just bouncing of the horizon for this "eternal equilibrium". Such a black hole will then evaporate by Hawking radiation, which is thermal. This again is not so clear, as the Polchinskypaper http://arxiv.org/abs/1207.3123 states immediately in the abstract: we want it to be a pure state! You are now claiming something that is not granted. When the black hole has completely evaporated, the net result will be the conversion of a pure state to a mixed state. For that, we clearly cannot use the static Schwarzschild solution, and just using KruskalSzekeres coordinates won't help since they still describe the same solution. Is there any closed form solution for the "transient black hole"? In any case I cannot quickly find it (so I can't even rule out it might fit in the margin of this post..) But we can look at Rindler coordinates for a uniformly accelerating frame. The Unruh effect corresponds to Hawking radiation and the Rindler horizon is the correct event horizon for the accelerating observer. Now, for the noneternal case, we only have to make the observer reduce its acceleration, corresponding to the black hole losing its mass. For the observer, the Rindler horizon fades away as acceleration is reduced (of course we get perturbed Rindler coordinates by the "variation of constant" method). So whatever matter was forever behind the horizon in the eternal case, will simply come into view again with non eternal acceleration. This is not yet the correct solution for the noneternal black hole, but it suggests that the paradox will be resolved just by allowing the black hole mass to decrease, which the correct solution must do. In any case, the event horizon cannot have the simple light like infinite wedge shape as it has for the eternal case. ... 2) But also that it is not lost because [...] Quantum mechanics is unitary. This means that the "finegrained" information in a quantum state is never lost; pure states evolve to pure states. Yes, this part we all want to keep. (It might even be true!) ... There are some obvious places to look for loopholes. I suspect that at least the obvious ones have all been analyzed to death, and all have unpleasant consequences. For instance, Hawking radiation might not really be thermal; but to get back enough correlations seems to require some very nonlocal interactions. That's not clear. if infalling information just bounces back at the horizon then that's local (as could happen in the eternal equilibrium hole). And if information in region II comes back into view by some curved shape of the noneternal horizon, then also nothing nonlocal is needed.. [...] The problem only appears quantum mechanically, when you allow black holes to evaporate thermally via Hawking radiation. And claiming that Hawking radiation is a pure state, statement i) in the above Polchinsky paper, does not avoid the paradox either. I would really like to see a diagram/coordinate system describing the noneternal black hole for a better judgement!  Jos 
Ads 
#12




Paradox unexplained
There are a couple of things to keep in mind when discussing
this problem. First, in classical general relativity the horizon is empty space  there's nothing material there. Second, for a large black hole, the curvature at the horizon is very small. That means that, by the equivalence principle, a freely falling (classical) observer will notice nothing special happening as she crosses the horizon. The consistent problem with many proposed "solutions" to the information loss paradox is that they require drastic changes in the physics in these empty, low curvature regions that are, at least classically, locally indistinguishable from anywhere else. On 4/15/16 8:24 AM, Jos Bergervoet wrote: On 4/3/2016 11:32 PM, Steven Carlip wrote: On 4/1/16 4:47 PM, Jos Bergervoet wrote: For the black hole information paradox I would expect two seemingly conflicting results (as is necessary for a paradox by definition,) e.g. like: 1) We know that information is lost because [...] We believe that matter in a pure quantum state can collapse to form a black hole. This is not quite clear if we cannot provide the solution of the GR equations that show the formation (so indeed we now can only say that we "believe" it). Well, we can certainly write a classical solution in which matter collapses to form a black hole. We can also make this "semiclassical"  that is, we can write down a quantum state describing, say, a thin shell of radiation and use the expectation value of its stressenergy tensor as a source. Now, it *could* be that if we could somehow carry out this same analysis in a completely quantum mechanical setting, the results might be completely different. There are proposals along this line, such as the "fuzzball" proposal of Mathur et al. But if that's the answer, you have to explain why the semiclassical approximation breaks down so drastically in a region in which space is empty and curvatures can be arbitrarily small  that is, why the correspondence principle of quantum mechanics fails in a place where there's no obvious reason it should fail. [...] Such a black hole will then evaporate by Hawking radiation, which is thermal. This again is not so clear, as the Polchinskypaper http://arxiv.org/abs/1207.3123 states immediately in the abstract: we want it to be a pure state! You are now claiming something that is not granted. You can *calculate* Hawking radiation, using what are now standard methods of quantum field theory in a curved background. The result is definitely not a pure state. Again, it could be that this calculation is badly wrong. But, again, the problem is to explain *why* it's wrong. Note that it's not enough to simply have "a pure state"  for the process to be unitary, one must have a *different* pure state for each possible initial state of collapsing matter. This almost certainly means that "late" Hawking radiation, emitted near the end of evaporation, must be correlated with much "earlier" Hawking radiation. But late Hawking quanta are never in causal contact with early quanta. So this would seem to require some highly nonlocal interactions. This would mean a breakdown of the effective field theory description, again in a place where curvatures are small and there's no evident reason for the description to break down. When the black hole has completely evaporated, the net result will be the conversion of a pure state to a mixed state. For that, we clearly cannot use the static Schwarzschild solution, and just using KruskalSzekeres coordinates won't help since they still describe the same solution. Is there any closed form solution for the "transient black hole"? There are many proposals. We have no idea which, if any, of them is correct. In any case I cannot quickly find it (so I can't even rule out it might fit in the margin of this post..) But we can look at Rindler coordinates for a uniformly accelerating frame. The Unruh effect corresponds to Hawking radiation and the Rindler horizon is the correct event horizon for the accelerating observer. Now, for the noneternal case, we only have to make the observer reduce its acceleration, corresponding to the black hole losing its mass. For the observer, the Rindler horizon fades away as acceleration is reduced (of course we get perturbed Rindler coordinates by the "variation of constant" method). So whatever matter was forever behind the horizon in the eternal case, will simply come into view again with non eternal acceleration. This is not yet the correct solution for the noneternal black hole, but it suggests that the paradox will be resolved just by allowing the black hole mass to decrease, which the correct solution must do. Many people have tried this. It's very hard (so far, not possible) to get it to work. In simple models one can calculate quantitatively exactly what sorts of interactions in the late stages of evaporation are needed to "purify" the earlier Hawking radiation. (Eugenio Bianchi has some nice work on this.) The answer seems to be that either normal Hawking evaporation has to change drastically while the black hole is still very large  again, when there is no apparent reason to expect the semiclassical description to fail  or else one needs to end with a very longlived, extremely high entropy "remnant." [...] 2) But also that it is not lost because [...] Quantum mechanics is unitary. This means that the "finegrained" information in a quantum state is never lost; pure states evolve to pure states. Yes, this part we all want to keep. (It might even be true!) Or might not  this is as much of a possible loophole as anything else. There are some obvious places to look for loopholes. I suspect that at least the obvious ones have all been analyzed to death, and all have unpleasant consequences. For instance, Hawking radiation might not really be thermal; but to get back enough correlations seems to require some very nonlocal interactions. That's not clear. if infalling information just bounces back at the horizon then that's local (as could happen in the eternal equilibrium hole). That makes no sense. There's nothing *at* the horizon. It's just empty space. It's true that "new" matter falling in can interact with Hawking radiation coming out  this is something 't Hooft has been working on lately  but I don't see how it's relevant to the setting in which the paradox is posed, which is a black hole forming from collapse of a pure state and then evaporating. And if information in region II comes back into view by some curved shape of the noneternal horizon, then also nothing nonlocal is needed.. Again, the devil is in the details. No one has managed to make a model in which this works without drastically changing the physics in low curvature, nearly classical regions where there seems to be no reason for it to change. That is, either the information in region II has to reappear very early on, when the black hole is still very large and quantum effects should be negligible; or else it has to stay "in view" for an extremely long time after the black hole has gotten very small, basically stretching out the black hole lifetime to nearly infinity and creating all sorts of problems associated with ultrahigh entropy "remnants." It's easy to identify assumptions and say, "Maybe this one is wrong" or "maybe that one is wrong." It's a whole lot harder to identify a plausible reason that any of the assumptions is wrong, and harder yet to actually show that that solves the problem. Steve Carlip 
#13




Paradox unexplained
Op vrijdag 8 april 2016 10:01:20 UTC+2 schreef Steven Carlip:
On 4/7/16 4:13 AM, Nicolaas Vroom wrote: Op zondag 3 april 2016 23:33:21 UTC+2 schreef Steven Carlip: We believe that matter in a pure quantum state can collapse to form a black hole. This is in a certain sense equivalent that a star collapses and becomes a neutron star Not really. A collapsing star is very unlikely to be in a pure quantum state. The whole question becomes: what is a pure quantum state versus a nonpure (mixed?) quantum state. Does it physical make sense to talk about a pure quantum state except under laboratory conditions? Such a black hole will then evaporate by Hawking radiation, which is thermal. This is in a certain sense equivalent that a star explodes and becomes a super novae. No. Here things are very different, because a black hole has an event horizon. Think of the first photon coming out of a supernova. etc A black hole is different. The first photon of Hawking radiation etc IMO (here I have to be very carefull) the concept of correlation is very difficult, because you have to define what you mean in this specific context and how it is measured. IMO the issue is much the type of particles or energy range of photons that can be emitted from any object. This diversity is a function of the processes that happen inside an object. How larger this diversity how more information is available. How smaller this diversity it is the opposite. The issue is if in either of these cases you can speak about information loss? In the first case, there's "coarse grained" information loss  it's *hard* to recreate the state of the star by looking at the correlations among the photons that come out. But it's not impossible. In the second case, the conventional picture of Hawking radiation implies that there is no correlation among the photons, so the information is genuinely completely lost. I agree with the conclusion but not with your reasoning. To answer the questions you must have a clear definition of what information means and what a pure and mixed quantum states are. Yes, but this is standard quantum mechanics. I agree for laboratory conditions. The concepts are very tricky in reality, related to actual objects in space. My interpretation of a mixed state is that it has a structure. For example in the Sun and in planets when you "travel" towards the center the density changes. This is also not what the term means. There's a nice explanation in the Wikipedia page under "Density matrix." If you want to talk about the black hole information paradox, you need to use the correct definitions. I fully agree with you. The practical problem is what is the density matrix of a BH? of a star, a sun, a planet The issue is here how do we know that BH physical can evaporate and change into a gaseous (visible?) state. "Evaporation" here has nothing to do with "gaseous"  it just means that the mass of black hole is converted completely to Hawking radiation. How do we know this happens? By doing a computation in quantum field theory to predict the evolution of a black hole. Now, the answer to the paradox may be that we're doing the computation wrong, but that's not a real answer unless you can say exactly *where* the computation is going bad. The real answer should be to make a prediction about the evolution of an object (BH) which we should be able to verify The problem is that that is very difficult for a BH. For example it is impossible(?) to demonstrate that a BH has evolved from something into "nothing" i.e. Hawking radiation In practice this means that it is very difficult to claim that the computation is right or wrong. The problem only appears quantum mechanically, when you allow black holes to evaporate thermally via Hawking radiation. The problem is much more a physical, chemical problem. No, it's not. You are free to invent a different problem, but that's not the one that's called the black hole information paradox. The evolution of a BH is a physical issue. I do not see in principle any problem that a BH completely evaporates. The problem starts, when it is possible to verify such a process (sequence of events) that this should not be in conflict with other laws. Nicolaas Vroom 
#14




Paradox unexplained
Op zaterdag 16 april 2016 08:38:51 UTC+2 schreef Steven Carlip:
First, in classical general relativity the horizon is empty space  there's nothing material there. Second, for a large black hole, the curvature at the horizon is very small. Snip You can *calculate* Hawking radiation, using what are now standard methods of quantum field theory in a curved background. The result is definitely not a pure state. Again, it could be that this calculation is badly wrong. But, again, the problem is to explain *why* it's wrong. The first thing is to verify why your calculation is correct. For example you have to very that the BH "emits" radiation. and that the predicted energy range is correct. That's not clear. if infalling information just bounces back at the horizon then that's local (as could happen in the eternal equilibrium hole). That makes no sense. There's nothing *at* the horizon. It's just empty space. It's true that "new" matter falling in can interact with Hawking radiation coming out  this is something 't Hooft has been working on lately  but I don't see how it's relevant to the setting in which the paradox is posed, which is a black hole forming from collapse of a pure state and then evaporating. Gerard 't Hooft at page 43/44 of this document: http://www.staff.science.uu.nl/~hoof...cturenotes.pdf discusses the same issue. IMO the evolution of a BH is a very complex lengthy process. When you consider the sketch of a BH in: https://astronomynow.com/2016/03/11/...veblackhole/ the center is completely black i.e. empty. The question is if that is true. I doubt that. One question is: if there is empty space around a BH. At page 29 G'tH writes: " Thus, as soon as matter falls in, the marginally trapped surface is replaced by a larger one. We can therefore conclude that the area of the horizon increases when matter falls in." Which implies that the region is not empty. At page 42/43 G'tH writes: "According to Hawking's derivation of the radiation process, any black hole, regardless its past, ends up as a thermodynamically mixed state. Would this also hold for a black hole that started out as a collapsing star in a quantum mechanically pure state? Can pure states evolve into mixed states? Not according to conventional quantum mechanics." Immediate next he writes: "From a physical point of view, the distinction between pure states and mixed states for macroscopic objects is pointless. Black holes should be regarded as being macroscopic." I agree with this last sentence. In a sense it removes the problem what pure and mixed states are. That is why I wrote in a previous posting: The problem is much more a physical, chemical problem. At the same time it is also an information problem in the sense that we cannot directly observe a BH. That means it is extremely difficult to observe that the life cycle time of a BH is finite. It is a murder without a body. For a star this is much simpler. Nicolaas Vroom 
#15




Paradox unexplained
On 4/16/2016 8:38 AM, Steven Carlip wrote:
There are a couple of things to keep in mind when discussing this problem. First, in classical general relativity the horizon is empty space  there's nothing material there. Second, for a large black hole, the curvature at the horizon is very small. That means that, by the equivalence principle, a freely falling (classical) observer will notice nothing special happening as she crosses the horizon. This of course makes it likely that the whole firewall idea was meant as a provocation. (The intended message may have been "Compared to the other alternatives this is still the most likely one, so imagine how bad things are!") The consistent problem with many proposed "solutions" to the information loss paradox is that they require drastic changes in the physics in these empty, low curvature regions that are, at least classically, locally indistinguishable from anywhere else. But some of those solutions might perhaps still work if the "firewall" exists not exactly at the Schwarzschild radius (since indeed there is nothing special there.) The supertranslations, for instance, are probably everywhere in space. (But that was a question I already asked in a separate thread, since the topic here is about the precise definition of the problem and the supertranslations are, or at least taste like, some solution!) .... Well, we can certainly write a classical solution in which matter collapses to form a black hole. We can also make this "semiclassical"  that is, we can write down a quantum state describing, say, a thin shell of radiation and use the expectation value of its stressenergy tensor as a source. You then start with the Vaidya model, I presume (as the Hawking PerryStrominger paper in their first example). But we should use the quantummechanical amplitude distribution of the fields that are the source (as opposed to merely expectation values) and thus arrive at a quantumgravity description.. Now, it *could* be that if we could somehow carry out this same analysis in a completely quantum mechanical setting, the results might be completely different. Something like the MerminWagner 2D instability could perhaps create a "firewall" after all! But I don't see how anything special exactly on the Schwarzschild radius could be explained. (Surely Polchinski must be joking, I still think.) ... Such a black hole will then evaporate by Hawking radiation, which is thermal. This again is not so clear, as the Polchinskypaper http://arxiv.org/abs/1207.3123 states immediately in the abstract: we want it to be a pure state! You are now claiming something that is not granted. You can *calculate* Hawking radiation, using what are now standard methods of quantum field theory in a curved background. The result is definitely not a pure state. The basic definition of quantum field theory is a quantized string which is in a pure state. (Weinberg vol. 1, Sect. 1.2, "The birth of quantum field theory.") If you calculate merely expectation values you don't calculate the actual time evolution of the actual quantum field. .. This almost certainly means that "late" Hawking radiation, emitted near the end of evaporation, must be correlated with much "earlier" Hawking radiation. Of course. And a deterministic time evolution guarantees that all Hawking radiation in the end is exactly correlated to the initial pure state, so there is no problem. (Unless we mess with the unitarity, but why would we?) Our only problem is to seek out the path of the information flow without nonlocal jumps. It's a topological problem. But late Hawking quanta are never in causal contact with early quanta. They certainly are, since QFT is causal. No quanta will be created unless at the same event others are annihilated. There is an unbroken chain of events. That is what the terms in the Lagrangian do in a *local* quantum field theory. And our standard model is a local QFT. .. So this would seem to require some highly nonlocal interactions. This would mean a breakdown of the effective field theory description, If the supertranslations effectively make a copy of passing early quanta then the information is available. The nocloning theorem might not apply (like in a CNOT gate) if they just entangle the information (with a pure gauge, or zero photon, whatever) which *still* is deterministic, unitary timeevolution. again in a place where curvatures are small and there's no evident reason for the description to break down. As the Hawking paper says, it's not yet an exact explanation of how the information flow works (in any case the paper does not attempt to depict the exact flow) but it opens some new possibilities. .... For that, we clearly cannot use the static Schwarzschild solution, and just using KruskalSzekeres coordinates won't help since they still describe the same solution. Is there any closed form solution for the "transient black hole"? There are many proposals. We have no idea which, if any, of them is correct. The Penrose diagram of the causal structure of the transient black hole, as I understand it, is like this: http://i.stack.imgur.com/Qtjrx.png But in HawkingPerryStrominger Fig. 2 they have another which looks more weird. Whereas their Fig. 1 (for the Vaidya model) seems normal. I also have nothing against there time split and "turnon" of evaporation. What I don't understand in Fig. 2: 1)Why is the singularity not shown? It exists in a seperate region of the manifold in http://i.stack.imgur.com/Qtjrx.png but Hawking et al. seem to ignore its presence. 2) Why are there curved corners in the inner square? If that's the horizon, it should be lightlike and keep its diagonal direction until its 2sphere size vanishes (but then the evaporation would be finished, which is not what the drawing suggests). ... That's not clear. if infalling information just bounces back at the horizon then that's local (as could happen in the eternal equilibrium hole). That makes no sense. There's nothing *at* the horizon. OK, there can't be a firewall or anything special there, so if we assume that matter falling in will be locked in a remnant but information about it remains outside, it's solved. So what was wrong with just accepting a remnant disjunct from our universe? You still can have Hawking radiation. You still can have the infalling matter encoding purestate Hawking radiation. It's all about keeping some information outside. What Fig. 2 in the paper seems to suggest that *not only* the information paradox is solved, but also the remnant is non existent! I feel like I could (given some time) understand the former, but not the latter. What am I missing? (Yes, lots of things, probably. :) )  Jos 
#16




Paradox unexplained
In article ,
Nicolaas Vroom writes: You can *calculate* Hawking radiation, using what are now standard methods of quantum field theory in a curved background. The result is definitely not a pure state. Again, it could be that this calculation is badly wrong. But, again, the problem is to explain *why* it's wrong. The first thing is to verify why your calculation is correct. For example you have to very that the BH "emits" radiation. and that the predicted energy range is correct. If the calculation is correct, then the radiation is essentially undetectable for all but the smallest black holes. So, while one could verify it in principle, in practice one cannot verify it directly. the center is completely black i.e. empty. The question is if that is true. I doubt that. Apply your own standards. You don't even have a calculation. At least provide something better than "I doubt that" to support your claim. One question is: if there is empty space around a BH. At page 29 G'tH writes: " Thus, as soon as matter falls in, the marginally trapped surface is replaced by a larger one. We can therefore conclude that the area of the horizon increases when matter falls in." Which implies that the region is not empty. Not necessarily. At least classically, it reaches the singularity in a finite time, so the volume just beyond the horizon is empty except just after something has fallen in. 

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