Preliminaries
Last time, we finally arrived at the diagram of the evaporating black hole:
More precisely, it's a non-rotating uncharged black hole.
The most important features of this spacetime are that it has a (spacelike) singularity and an event horizon. The blue line indicates the surface of some collapsing matter configuration [1]. Let me remind you that since we've chosen radial coordinates, curves that pass through r=0 (where it is non-singular) look like they are reflected back. These segments of curves are also referred to as in- and outgoing in an obvious terminology.
Shown in the figure is v0, the last ray of light that passes through the collapsing matter and still manages to escape [2]. In the background depicted in the diagram, particle creation takes place at the horizon, which causes the black hole to lose mass. It then shrinks until it has finally completely evaporated, leaving behind nothing but thermal Hawking radiation [3].
Another important fact is that this spacetime is "asymptotically flat" or "asymptotically Minkowski," which means that at an infinite distance from the black hole spacetime is flat (flat as in "the curvature tensor vanishes"). This doesn't necessarily have to be the case (i.e. it could be asymptotically AdS instead), but it will make our discussion leaner. The reason for this asymptotic flatness is simply that in the beginning as well as in the end the matter is arbitrarily thinly dispersed.
To wrap up the summary, note that this diagram depicts a highly idealized situation. It's an evaporating black hole in an otherwise entirely empty spacetime. Realistic black holes are surrounded by matter and accrete mass, and occasionally Bob sends one of his Alices behind the horizon. But, as so often in physics, the uncluttered idealized version will help us understand the situation better without spoiling the conclusions.
Evolution
To understand the black hole information loss problem you need one further ingredient, that's what physicists mean with time-evolution. Intuitively, it means that one specifies a system at one moment in time, known as "initial conditions" and from this determines the status of that system at any other time by the help of a differential equation [4]. The most basic example is throwing a ball. The initial conditions needed are the location and velocity at one moment. The equation you use is Newton's law (or something equivalent).
In General Relativity the situation is more complicated but conceptually similar. You specify the initial conditions of your matter configuration at one moment in time and use Einstein's field equations to determine what space-time and matter are doing at any other time [5]. The attentive reader might remark that already in Special Relativity "one moment in time" is ambiguous. Indeed, and this is also the case in General Relativity. Point is, you can use any "moment in time" for you initial conditions, as long as it's at one moment, but everywhere in space (this is not the only option, but the most commonly used one). We call that a "complete spacelike hypersurface." Complete means basically it doesn't have holes and no expandable boundaries.
Almost there now. In the below picture I've added two complete spacelike hypersurfaces denoted Σ1 and Σ2
Information Loss
The evolution of a quantum mechanical state is unitary. That means in particular it is time-reversible [6]. You can evolve the status of your system back and forth how you like. There are many ways to think about information, and when talking about the black hole evolution some people like to hang themselves up on the exact meaning of information. That's a very interesting topic, but we'll cut this discussion short because it's irrelevant to understand the problem. Consider you have an initial state and you evolve it into a final state. If your final state does not uniquely specify the initial state we'll consider this loss of information. It means you can't tell what happened.
Black hole evaporation causes a loss of information because the outgoing radiation depends only on the total mass. Once the black hole is evaporated, all states with the same initial mass are converted into the same endstate. There are many ways a system can be composed if you only know the total mass [7]. There's only one way it will look after evaporation. This process is thus not reversible: it is not possible to reconstruct the initial state from the final state. But if it's not reversible, it can't be unitary. And for beginners that's the problem: The formation and complete evaporation of the black hole seems to be incompatible with quantum mechanics. On the advanced level it's more complicated since we know the computation leading to Hawking radiation breaks down when quantum gravity becomes important. In this case the problem is that this quantum gravitational contribution doesn't help you to get enough information out.
There are several points that people tend to misunderstand about the problem already on the beginner's level, so let me mention some pitfalls. First, note that the problem is not that the information is inaccessible behind a horizon. There is no horizon in the endstate, look at the diagram. It's flat Minkowski space with infinitely thinly dispersed thermal radiation. Think of the black hole as a black box. You start with flat Minkowski space, something happens in between, you end with flat Minkowski space. Yet, this evolution cannot be described by quantum mechanics as we know it. Second, to lay out the problem I didn't have to refer to measurement at all. It's a fundamental incompatibility in the evolution, you don't solve that incompatibility by waving your hands and yelling "measurement problem." Third, we are talking about the microscopic laws. Yes, on macroscopic scales we do have an arrow of time and entropy tends to increase anyway, but the problem is to accommodate the black hole evolution with the fundamentals of quantum mechanics prior to coarse graining. Fourth, yes, it is possible to cover the the Schwarzschild geometry by what is known as "nice slices," hypersurfaces that avoid the singularity for any finite time. (You find some very good graphics for that here, on slide 10). That doesn't solve the problem either because no matter how you turn it, your black hole evaporates away and you'll finally have to face that all you have left at scri minus is thermal radiation.
If you want to argue that the problem is a thought-experiment and unobservable, please read my earlier post on Thoughts and Experiments. We have to pay attention to inconsistencies even if they are not observable since they document a gap in our knowledge. While troubelsome, they also offer us opportunities to improve our understanding of Nature, which is why physicists turn problems like this upside-down and inside-out.
The value of the causal diagram once again is that it captures a lot of physics in one simple picture. If you look at it one more time you can see the problem. At the singularity matter gets crushed to infinite density and absent non-local effects everything that crossed the horizon has to fall into the singularity. Recall that curves on 45° angles depict the trajectories light travels on. You'd have to be faster than light to avoid the singularity once you've passed the horizon. All information about the initial state that evolves into the singularity is thus not available on the final slice. And that's exactly what happens in the calculation. You have to finally let go of the part of the initial wave-function that vanished behind the horizon, because it cannot avoid the singularity.
Now what
This then opens the playground for solutions to the problem. You either have to get the information out before it hits the singularity or avoid that it crosses the horizon at all. Lee and I argued in our last year's paper (see previous post for details) that the easiest way to avoid hitting the singularity is if there is no singularity. This by itself doesn't mean information behind the horizon becomes accessible again for the observer outside the horizon. But if you recall, this wasn't the problem to begin with. The problem was to achieve compatibility with unitary evolution, and this doesn't require information to be accessible to everybody as long as it exists.
In any case, since the black evaporation is and will likely remain elusive to experiment, everybody has their favorite solution. String theorists like the idea that information never gets lost because the evolution of the black hole is equivalently described by a dual, unitary, theory formulated on the boundary of the space-time which has been shown to encode regions of the bulk both inside and outside the horizon. People working on other approaches to quantum gravity seem to favor the idea that the singularity is avoided and the information somehow makes it out of the horizon, though at least to me it's remained unclear how so. (I sometimes suspect they'll finally reinvent and adopt the string theory solution.) Scenarios with stable or quasi-stable remnants that keep information or slowly release it also occasionally reoccur, and then there's parallel- and baby universes and a long list of miscellaneous other. The idea that black holes can't be formed to begin with lies in a shadowy fringe-area and is not considered plausible by the vast majority of researchers in the field.
Information Loss
The evolution of a quantum mechanical state is unitary. That means in particular it is time-reversible [6]. You can evolve the status of your system back and forth how you like. There are many ways to think about information, and when talking about the black hole evolution some people like to hang themselves up on the exact meaning of information. That's a very interesting topic, but we'll cut this discussion short because it's irrelevant to understand the problem. Consider you have an initial state and you evolve it into a final state. If your final state does not uniquely specify the initial state we'll consider this loss of information. It means you can't tell what happened.
Black hole evaporation causes a loss of information because the outgoing radiation depends only on the total mass. Once the black hole is evaporated, all states with the same initial mass are converted into the same endstate. There are many ways a system can be composed if you only know the total mass [7]. There's only one way it will look after evaporation. This process is thus not reversible: it is not possible to reconstruct the initial state from the final state. But if it's not reversible, it can't be unitary. And for beginners that's the problem: The formation and complete evaporation of the black hole seems to be incompatible with quantum mechanics. On the advanced level it's more complicated since we know the computation leading to Hawking radiation breaks down when quantum gravity becomes important. In this case the problem is that this quantum gravitational contribution doesn't help you to get enough information out.
There are several points that people tend to misunderstand about the problem already on the beginner's level, so let me mention some pitfalls. First, note that the problem is not that the information is inaccessible behind a horizon. There is no horizon in the endstate, look at the diagram. It's flat Minkowski space with infinitely thinly dispersed thermal radiation. Think of the black hole as a black box. You start with flat Minkowski space, something happens in between, you end with flat Minkowski space. Yet, this evolution cannot be described by quantum mechanics as we know it. Second, to lay out the problem I didn't have to refer to measurement at all. It's a fundamental incompatibility in the evolution, you don't solve that incompatibility by waving your hands and yelling "measurement problem." Third, we are talking about the microscopic laws. Yes, on macroscopic scales we do have an arrow of time and entropy tends to increase anyway, but the problem is to accommodate the black hole evolution with the fundamentals of quantum mechanics prior to coarse graining. Fourth, yes, it is possible to cover the the Schwarzschild geometry by what is known as "nice slices," hypersurfaces that avoid the singularity for any finite time. (You find some very good graphics for that here, on slide 10). That doesn't solve the problem either because no matter how you turn it, your black hole evaporates away and you'll finally have to face that all you have left at scri minus is thermal radiation.
If you want to argue that the problem is a thought-experiment and unobservable, please read my earlier post on Thoughts and Experiments. We have to pay attention to inconsistencies even if they are not observable since they document a gap in our knowledge. While troubelsome, they also offer us opportunities to improve our understanding of Nature, which is why physicists turn problems like this upside-down and inside-out.
The value of the causal diagram once again is that it captures a lot of physics in one simple picture. If you look at it one more time you can see the problem. At the singularity matter gets crushed to infinite density and absent non-local effects everything that crossed the horizon has to fall into the singularity. Recall that curves on 45° angles depict the trajectories light travels on. You'd have to be faster than light to avoid the singularity once you've passed the horizon. All information about the initial state that evolves into the singularity is thus not available on the final slice. And that's exactly what happens in the calculation. You have to finally let go of the part of the initial wave-function that vanished behind the horizon, because it cannot avoid the singularity.
Now what
This then opens the playground for solutions to the problem. You either have to get the information out before it hits the singularity or avoid that it crosses the horizon at all. Lee and I argued in our last year's paper (see previous post for details) that the easiest way to avoid hitting the singularity is if there is no singularity. This by itself doesn't mean information behind the horizon becomes accessible again for the observer outside the horizon. But if you recall, this wasn't the problem to begin with. The problem was to achieve compatibility with unitary evolution, and this doesn't require information to be accessible to everybody as long as it exists.
In any case, since the black evaporation is and will likely remain elusive to experiment, everybody has their favorite solution. String theorists like the idea that information never gets lost because the evolution of the black hole is equivalently described by a dual, unitary, theory formulated on the boundary of the space-time which has been shown to encode regions of the bulk both inside and outside the horizon. People working on other approaches to quantum gravity seem to favor the idea that the singularity is avoided and the information somehow makes it out of the horizon, though at least to me it's remained unclear how so. (I sometimes suspect they'll finally reinvent and adopt the string theory solution.) Scenarios with stable or quasi-stable remnants that keep information or slowly release it also occasionally reoccur, and then there's parallel- and baby universes and a long list of miscellaneous other. The idea that black holes can't be formed to begin with lies in a shadowy fringe-area and is not considered plausible by the vast majority of researchers in the field.
I personally am somewhat agnostic on the how of information release, but am certain it can eventually only be achieved if the singularity is avoided (in the sense explained in mentioned paper.)
So. *wiping sweat off forehead* If you still haven't enough let me know.
[1] Modulo the question where it hits the singularity, see comments to previous post, but that's not relevant for our purposes.
[2] To be more precise, since we have assumed spherical symmetry to be able to draw a 4 dimensional manifold, a point in the figure is actually a sphere, but this distinction isn't so relevant. One can decompose the solutions to the wave-equation in spherical harmonics as usual. We are then talking here only about the s-wave state. States with higher angular momentum have a more complicated behavior.
[3] In the upheaval around the alleged risk of black holes at the LHC, some people ridiculed the fact that Hawking's calculation does not "automatically" decrease the mass of the black hole but that energy conservation is "put in by hand." That is in fact true. But that in this calculation the radiation does not "automatically" carry away the mass of the black hole is an artifact of doing the analysis in a fixed background, which "by hand" prohibits the mass from changing. There is absolutely nothing wrong with the argument that taking into account the energy loss through radiation the mass is not in fact constant. This in turn does not render the calculation false, it merely sets limits to its accuracy, and Hawking's calculation can be shown to be an excellent approximation as long as the ratio of mass loss is small. It is only in the end stage of evaporation when quantum gravity is important that the mass loss becomes relevant for the properties of the emitted radiation. This phase is thus still a matter of discussion.
[4] Note that it is entirely irrelevant the "initial" conditions are indeed the beginning of the evolution from which you determine the past. You could equally well specify the state of your system in the future and evolve it into the past.
[5] Note that this means once you've specified an equation of state for the matter, General Relativity does not allow you to specify what you want the matter to do over the course of time.
[6] The reverse is not true. A reversible evolution is in general not also unitary.
[7] Even if it's spherically symmetric. You lose all information in the radial direction.
[4] Note that it is entirely irrelevant the "initial" conditions are indeed the beginning of the evolution from which you determine the past. You could equally well specify the state of your system in the future and evolve it into the past.
[5] Note that this means once you've specified an equation of state for the matter, General Relativity does not allow you to specify what you want the matter to do over the course of time.
[6] The reverse is not true. A reversible evolution is in general not also unitary.
[7] Even if it's spherically symmetric. You lose all information in the radial direction.
Dear Bee,
ReplyDeleteThanks for returning to this topic!
A nitpick: The blue line indicates... - there is no blue line.
Best,
-Arun
Dear Arun,
ReplyDeleteThanks :-) Well, the line is blue. Or at least it was blue before I exported the jpg. But you're right it's hard to tell, next time I'll use a lighter shade. Best,
B.
Hi Bee,
ReplyDeleteThanks for spending the time and effort to complete your discussion of causal diagrams, as to how they’re used and the implications they have in regards to the information problem. It is also something I will admit to having to read and think about for some time to have it understood as well as it deserves. The bottom line of course here is as you pointed out, being that unless the minority opinion is correct that black holes simply can’t exist , that any direct imperial evidence to support what does or does not happen to the information seems beyond science’s capability.
Then of course this is not the only veil nature seems to have that resists our knowing, as there is much in Quantum theory that presents as the same. I’ve often wondered perhaps if this is being looked at from the wrong direction and that’s not to focus the effort in devising theories that nature needs to approve of, yet rather as J.S. Bell did to devise situations incorporating logical ways to have nature tell us what the answers might be. That’s what I think is so often missed as being the uniqueness of the Bell approach to problems, as not actually having an opinion as to be accepted or denied, by way of agreement with experiment, rather finding ways by which the question is answered in limiting experimental results as to what can serve as a reasonable conclusion. Actually when you think about it the Bell approach may be the only way physics can proceed much further in future if we are to extend our understanding much at all.
“Among the branches of philosophy, I had, at an earlier period, given some attention to logic, and among those of the mathematics to geometrical analysis and algebra, -- three arts or sciences which ought, as I conceived, to contribute something to my design. But, on examination, I found that, as for logic, its syllogisms and the majority of its other precepts are of avail- rather in the communication of what we already know, or even as the art of Lully, in speaking without judgment of things of which we are ignorant, than in the investigation of the unknown; and although this science contains indeed a number of correct and very excellent precepts, there are, nevertheless, so many others, and these either injurious or superfluous, mingled with the former, that it is almost quite as difficult to effect a severance of the true from the false as it is to extract a Diana or a Minerva from a rough block of marble.”
- René Descartes - Discourse on The Method: of Rightly Conducting The Reason, and Seeking Truth in the Sciences (1637)
Best,
Phil
Phil: Unless of course the LHC produces black holes :-p Best,
ReplyDeleteB.
Great post Bee!
ReplyDelete>> Black hole evaporation causes a loss of information because the outgoing radiation depends only on the total mass.
I wonder if you could put the problem this way: although there is an analogy between black holes and everyday thermodynamics at the level of laws, this analogy doesn't continue to the level of microscopic foundations. For example, we have the analogies:
black hole mass :: energy of a thermodynamic system
surface gravity :: temperature
guiding how we understand Hawking radiation. But these quantities are associated with macrostates. And the analogy breaks down at the "foundational" level of the microstates. In everyday thermodynamical systems, it's the evolution of microstates that determines what's "really" going on. We calculate their average behavior, and thus arrive at the laws of thermodynamics. But if the microstates of a black hole are described using classical parameters like momentum, charge and mass, then there doesn't seem to exist a non-trivial set of microstates at all. So, the foundations from which we derive the statistical behavior of a black hole must be very, very different than the foundations of everyday thermodynamics.
Hi Bryan,
ReplyDeleteYes, that's one way to think about it. Best,
B.
Thanks for that, Bee. I've got a few questions. I've always felt you've favoured the remnant solution - is that right? I'm not keen on it myself. Surely the black hole has to completely evaporate, doesn't it? How can a massive remnant be stable if it has an event horizon producing Hawking radiation?
ReplyDelete(Personally, I feel the holographic principle comes into play here. That's such an interesting result, that the information contained within a volume of space is proportional to the area of it's boundary. I think that's a good clue. I think the horizon can encode the information contained in the hole, or something like that.)
Hi Andrew,
ReplyDeleteA black hole remnant doesn't emit radiation. Remnants have Planck mass, meaning their horizon is in the quantum gravity regime. The idea is that the temperature could drop to zero. After all, we don't really know what actually happens. That a stable remnant remains is a possibility people have discussed as long as they've known black holes evaporate.
Not sure why you think I've favored the remnant solution. I'd much prefer complete evaporation, but not sure it's relevant what I prefer. Best,
B.
Thanks. I didn't know that a remnant is not supposed to emit radiation. I just thought you favoured the remnant idea after that paper you wrote with Lee which spent a fair bit of time defending the remnant idea. You say you're in favour of the "no singularity" idea (though I don't suppose that necessarily implies a remnant). I'll take it that you're agnostic about possible solutions.
ReplyDeleteDoes the remnant idea imply that all the information in a black hole can be packed into a Planckian volume? Or have I misunderstood. Thanks.
Hi Andrew,
ReplyDeleteWell, that the information remains inside the remnant is the reason people are discussing it as a solution. In the paper with Lee, we've simply stated that the reasons that have been put forward against remnants are inconclusive. That doesn't mean I favor this solution, I just think it's not so easy to dismiss it. Also, one of the problems with information recovery in the late stages is that it leads to a very long-lived, quasi-stable, remant (that however does eventually completely vanish). For this case, the objections against remnants would also apply. Best,
B.
Dear Bee,
ReplyDeleteThis question may really belong to the previous post on information loss.
Is it possible that we don't know how to describe the thermal state well and therein lies a resolution of the information loss problem? E.g., if all the radiation from the burning of a book (or better, its annihilation with anti-matter) is directed to a blackbody and all I can observe is the resulting blackbody radiation - nevertheless we would argue that there is no information loss here
Dear Arun,
ReplyDeleteIf you mean that there might be correlations in the thermal radiation that carry the missing information, this is certainly a possible solution people have considered (as you probably know). Question is of course, how does it get there, missing a causal relation to the inside of the horizon which requires large-scale non-locality. Best,
B.
Andrew, I think the horizon can encode the information contained in the hole
ReplyDeleteI've always wanted to read (but never did) "Black Holes - The Membrane Paradigm" by Thorne, Price and MacDonald.
I can only quote from the introduction: "The membrane paradigm is mathematically equivalent to the full general relativistic theory of black holes, so far as all the physics outside the horizon is concerned. ...More specifically, in this viewpoint particles and fields very near the horizon possess a highly complex, frozen "boundary-layer" structure, which is essentially a relic history of the black hole's past. This complex boundary layer has no influence on hte present or future evolution of particles and fields above the boundary layer; in a way the membrane viewpoint "stretches" the horizon to cover up the boundary layer and then imposes simple and elegant, membrane-like boundary conditions on the stretched horizon. This sweeping away of irrelevancies entails small (and in practice negligible) errors, but it results in a formalism and viewpoint remarkably powerful for astrophysical studies. Moreover, it acquires a special elegance when one recognizes that the entropy of a black hole is the logarithm of the total number of quantum-mechanically distinct configurations that could exist in the covered-up boundary layer."
"...But the membrane viewpoint loses its validity (indeed, even ceases to exist) inside the horizon. For example, an observer who falls through the horizon discovers that the horizon is not really endowed with electric charge and current; it merely looks that way from outside. Despite this ephemeral nature of the membrane, the researcher who takes it seriously and believes in it (if only temporarily, while working on a specific research project) may be rewarded with powerful insights".
---
Dear Bee,
ReplyDeleteI guess my first question is - how do I even go about finding possible correlations in seemingly thermal radiation?
What do I measure (or compute in a thought experiment)?
This comment has been removed by the author.
ReplyDeleteHi Arun,
ReplyDeleteWhat do I measure (or compute in a thought experiment)?
How about patterns that suggest they're not simply something of a random origin as J.S. Bell considered in respect to nailing down nature in relation to the quanta as being nonlocal.
Best,
Phil
P.S. Unlike my posts:-)
Thanks for that, Arun.
ReplyDeleteI think this is very interesting too: Elephant and the Event Horizon.
Peter Steinberg, when at Quantum diaries, lead us through this.
ReplyDeleteThe creepy part of these kind of discussions is that one doesn't say that RHIC collisions "create" black holes, but that nucleus-nucleus collisions, and even proton-proton collisions, are in some sense black holes, albeit black holes in some sort of "dual" space which makes the theory easier.
We all understand the clarifications that Peter helped to make, yes?:)Lawsuits and such producing fear in the public?
So you know what I mean by the geometric?
Lets say you have a trajectory in place traveling around the ring and there are calorimeters in place, what are these calorimeters used for?:)
Lets say "these trajectories" come to us from space are natural and come from such a location similar to what is produced by experiment. We do not tend to forget "the meeting point?"
So, what is produced in that moment, and how would the schematics of your example and the correlation given here serve to drawn similarities as to how one writes the info about microscopic black hole that quickly disseminate or large cosmological types that produce remnants for us in what is left in the bulk. CMAP
Frequently asked questions about LHC
The strongest limits on the amount of antimatter in our Universe come from the analysis of the diffuse cosmic gamma-rays arriving on Earth and the density fluctuations of the cosmic background radiation. If one assumes that after the Big Bang, the Universe separated somehow into different domains where either matter or antimatter was dominant, then at the boundaries there should be annihilation's, producing cosmic gamma rays. In both cases the limit proposed by current theories is practically equivalent to saying that there is no antimatter in our Universe.
As a beginner I am just trying to put it together. Thanks for your explanation. This is why I stick around:)
Best,
The Decay Chain
ReplyDeletedeconstruction: event display
Usually all physicists see are the remnants of a new particle decaying into other types of particles. From that, they infer the existence of the new species and can determine some of its characteristics.
Andrew,
ReplyDeleteSusskind knew exactly what was being proposed just as Seth Lloyd takes it one step further in luminance.
For Bryan....
The old version of string theory, pre-1995, had these first two features. It includes quantum mechanics and gravity, but the kinds of things we could calculate were pretty limited. All of a sudden in 1995, we learned how to calculate things when the interactions are strong. Suddenly we understood a lot about the theory. And so figuring out how to compute the entropy of black holes became a really obvious challenge. I, for one, felt it was incumbent upon the theory to give us a solution to the problem of computing the entropy, or it wasn't the right theory. Of course we were all gratified that it did. Black Holes and Beyond: Harvard's Andrew Strominger on String Theory
Best,
I think it's important to say that the Bekenstein Bound (the maximum information content of a volume of space is proportional to the area of the boundary) does not necessarily involve any string theory. It purely comes from considering black hole entropy, and it is well-established. I think it is important to keep that idea decoupled from string theory (the ideas are so commonly mixed-up, because of AdS/CFT which builds on the Bekenstein Bound).
ReplyDeleteI think the Bekenstein Bound is very important in that respect - one area of real progress in physics.
Re: the Elephant and the event horizon - what is the holographic equivalent of the event horizon?
ReplyDeleteI see there's a very nice simple derivation on the Bekenstein Bound (and the more general holographic bound which considers the maximum information content of any volume of space) here). Note it's just a consideration of black hole entropy - no string theory required.
ReplyDeleteArun, the idea of the "holographic universe" and AdS/CFT is a much more speculative idea (which does involve string theory) which suggests that all the information in the universe is encoded on the area of the boundary of our universe. This idea comes from the result that the information in a volume can be encoded on the area of the boundary of that volume. The idea is that our 5D universe is recorded like a hologram on a 4D surface at its periphery. But, like I say, this is all totally speculative. Not like the Bekenstein Bound, and the basic holographic bound result that the information in a volume can be encoded in the area of its boundary. Like I say, no string theory there.
ReplyDeleteOK, what is the speculative equivalent of an event horizon in bulk in the boundary theory? Simply as an object in the boundary theory - which is a quantum field theory in AdS/CFT it should be of considerable interest.
ReplyDelete---
Another thought - that may be wholly mistaken - regarding the Elephant and the Event Horizon. One problem as I see it is the way we do QFT is not inherently local. To do second quantization, we decompose a field into spacetime filling modes. In a sense, I have to know all the past, present and future. To do a path integral, too, I have to know all modes of the field. Only if we're lucky that a saddlepoint approximation to the path integral is good enough for the answer we want, we're stuck. (Maybe there is some other way of doing QFT - if so, I'd like to learn it.) I don't think anyone can take the equivalent of the elephant - even a simple hydrogen atom - and time-evolve it quantum mechanically as it falls through the horizon.
I don't know enough about the details of AdS/CFT - sorry. Way over my head!
ReplyDeleteFirst, the relativity of acceleration surely must mean that particles aren't created at the EH in an absolute sense. Their existence must be thought of relative to observer motion (not just their red or blue shift.) Yes, per implications of Unruh radiation being "felt" by accelerating observer as if from Rindler horizon, but not having objective existence to inertial bystanders who are oblivious to that observer's RH.) But that could just cause needless buzz since effectively the EH can "radiate."
ReplyDeleteMore peculiar to me is, what happens if the BH is charged? I don't see how that could prevent the radiation process from occurring (bad to have step function of amount of of charge.) But then if BH fully evaporates, how would the residual charge be presented? Sure people thought of this, I just don't know what they thought.
(PS I ctrl-f-ed for "charge" and didn't see enough answer.)
Okay to Bekenstein bound.
ReplyDeleteSpacetime in String theory More here
When looking at the image by Bekenstein one has to take in "where the strings are located," as well as, what "the soup" represents by Horowitz as to specify a 5d recognition?
Not that I want to confuse, but more that one understands where strings are and what the 2d approach represents on the horizon.
Is this better?
Thanks,
This comment has been removed by the author.
ReplyDeleteMost certainly the best tools are what can help extend our vision of what is not ultimately clear when taken in context of that 5d world.
ReplyDeleteToday, however, we do have the opportunity not only to observe phenomena in four and higher dimensions, but we can also interact with them. The medium for such interaction is computer graphics. Computer graphic devices produce images on two-dimensional screens. Each point on the screen has two real numbers as coordinates, and the computer stores the locations of points and lists of pairs of points which are to be connected by line segments or more complicated curves. In this way a diagram of great complexity can be developed on the screen and saved for later viewing or further manipulation
So abstract in fact you can take it for granted?:)
Taking in the greater perception of what consolidates too(extra dimensions), as we look to the result as if GR comes from a higher dimension?
It's just another way of looking at that 5d space?
Best
We all understand the reference to the elephant? We understand the reference of the elephant to quantum gravity?:)
ReplyDeleteOf course it's not easy, so we of course have to construct thought experiments.
The Blind Men and the Elephant
John Godfrey Saxe (1816-1887)
It was six men of Indostan
To learning much inclined,
Who went to see the Elephant
(Though all of them were blind),
That each by observation
Might satisfy his mind.
The First approached the Elephant,
And happening to fall
Against his broad and sturdy side,
At once began to bawl:
"God bless me! but the Elephant
Is very like a WALL!"
The Second, feeling of the tusk,
Cried, "Ho, what have we here,
So very round and smooth and sharp?
To me 'tis mighty clear
This wonder of an Elephant
Is very like a SPEAR!"
The Third approached the animal,
And happening to take
The squirming trunk within his hands,
Thus boldly up and spake:
"I see," quoth he, "the Elephant
Is very like a SNAKE!"
The Fourth reached out an eager hand,
And felt about the knee
"What most this wondrous beast is like
Is mighty plain," quoth he:
"'Tis clear enough the Elephant
Is very like a TREE!"
The Fifth, who chanced to touch the ear,
Said: "E'en the blindest man
Can tell what this resembles most;
Deny the fact who can,
This marvel of an Elephant
Is very like a FAN!"
The Sixth no sooner had begun
About the beast to grope,
Than seizing on the swinging tail
That fell within his scope,
"I see," quoth he, "the Elephant
Is very like a ROPE!"
And so these men of Indostan
Disputed loud and long,
Each in his own opinion
Exceeding stiff and strong,
Though each was partly in the right,
And all were in the wrong!
So how shall we describe that 5d space? If there is no singularity. How do we match correlative phenomenological relations to these thoughts?
There is no information loss?
Imagine what ruminative values once electromagnetism and gravity are joined.
Best,
Gedanken Experiments Involving Black Holes
ReplyDeleteABSTRACT
Analysis of several gedanken experiments indicates that black hole complementarity cannot be ruled out on the basis of known physical principles. Experiments designed by outside observers to disprove the existence of a quantum-mechanical stretched horizon require knowledge of Planck-scale effects for their analysis. Observers who fall through the event horizon after sampling the Hawking radiation cannot discover duplicate information inside the black hole before hitting the singularity. Experiments by outside observers to detect baryon number violation will yield significant effects well outside the stretched horizon.
Dear Arun,
ReplyDeleteI would suggest you sit on some shell around the black hole, capture all the radiation it emits, measure the details and then look for correlation (n-point). Best,
B.
Andrew, Arun: The horizon provides a non-zero temperature for the CFT. Best,
ReplyDeleteB.
Neil: You are right, it is in fact very sloppy to say the particles are created "at" the horizon since they do have an uncertainty comparable to the size of the black hole. You are also right with that the notion of particles is observer dependent, that is in fact which causes the Unruh effect. Charged black holes radiate off their charge and then proceed like usual. Since we don't know any massless charged particles, you can however construct the following problem (that has been around since some decades I believe). If you have a charged black hole that evaporates off mass without losing its charge till it is lighter than the lightest charged particles, what do you do? The problem however doesn't even make a good paradox because the electron mass is so tiny the black hole would have reached Planckian curvature long before it arrives at electron mass. Best,
ReplyDeleteB.
Tx Bee, that is good to find basic concurrence on the particle and horizon issue. As for charge: My understanding is, a BH evaporates entirely not just to the Planck mass; as per Wikipedia:
ReplyDelete...with the most likely endpoint being the dissolution of the black hole in a violent burst of gamma rays.
Well maybe charge affects that somehow, but otherwise an exploded BH has the charge problem.
Neil: What I was saying is if the black hole has shrunk to Planck mass, the curvature is in the Planckian regime and quantum gravitational effects become relevant. Absent a theory for quantum gravity, nobody knows what really happens. Most people in the field believe the black hole does entirely decay, yet the exact process is unclear. One alternative option is that it does not decay but leaves a stable Planck-mass "remnant" behind (see above exchange with Andrew). Best,
ReplyDeleteB.
Hi Bee,
ReplyDeleteThe horizon provides a non-zero temperature for the CFT.
Is that all that the horizon does?How do I locate the horizon in the AdS given a non-zero temperature in the CFT? It could be anywhere. Also, I can have, I hope, two different long-lived blackholes with two different horizon temperatures. Do we know how to do out-of-thermal equilibrium thermal QFT?
----
Unrelated question - what does a Higgs-like spontaneous symmetry breaking in the AdS show up as in the CFT?
Arun: It's spherically symmetric. Knowing the temperature fixes the location.
ReplyDelete1. Wouldn't most of the information be radiated away before the matter falls behind the event horizon, as the matter falls into the black hole?
ReplyDelete2. If a black hole has a quantum description, then it must be described by a set of states, including a ground state, where the observables are total spin, charge, color, mass, etc... But then the black hole can only lose mass by transitioning through specific energy levels, which means that the radiation is not a perfect black body and must carry information?
Perhaps I'm to naive?
Aaron: 1) Questions of "when" are observer dependent in GR. In the eigentime of the collapsing particles the amount of energy loss before horizon crossing is negligible. For the observer at asymptotic infinity, the radiation is created when and where the matter crosses the horizon. 2) You are right that the black hole's radiation is actually quantized. It is strictly speaking only a smooth blackbody curve for arbitrarily large holes (where you don't notice the quantization). That doesn't mean that it carries additional information, it just means the emission is discrete but takes place according to a random variable. Best,
ReplyDeleteB.
Ah, but you cannot speak of the eigen-time (more precisely its complement of energy) of an inwardly falling observer because of the Unruh effect, which shows that the classical momentum operators do not commute in a heavily curved spacetimes. Basically an inwardly falling observer loses the ability to tell 'where' his energy is.
ReplyDeleteAaron: The eigentime is defined via the geodesics in what is by assumption a classical background, this is what I was referring to. You were asking about the when, not about the where. Besides this, the idea that the information is all radiated off before the matter reaches the horizon is one of the less frequently discussed options, it's commonly referred to as "bleaching." The problem is not the idea itself, which I have a big deal of sympathy for, but that a mechanism is missing. Hawking's calculation is very robust and doesn't leave you sufficient space to get any additional information in the radiation without a drastic change of physics in regimes where we don't expect any change. Best,
ReplyDeleteB.
I don't think complete bleaching will pan out, but I think that all the information that cannot be gained by carefully observing the transitions of the black hole would be bleached.
ReplyDeleteAfter all, given the strength of the virtual particle bath near a black hole the chance that any particle even one that is directly inwardly falling, would not get scattered is virtually nil. But that means that once the curvature is strong enough, the source of the curvature becomes close to a perfect (random) scattering surface, bouncing around in Brownian motion.
Aaron: I think you have a totally wrong impression of the "strength" of the effect. It's tiny. It's tiny because the curvature on the horizon can be as small as you want it to be. You also seem to think that the Hawking radiation is mostly produced somehow "inside" the collapsing matter. In fact however, the by far largest contribution comes from the surface at horizon formation. This is exactly the reason why the only quantity that finally enters the spectrum is the surface gravity. You have put your finger on exactly the right spot, this is where the problem originates, but putting the finger there doesn't solve the problem. Best,
ReplyDeleteB.
Limiting the curvature at the horizon to zero sounds like having your cake and eating it to:
ReplyDeleteThe Hawking Effect for Schwarzschild observer is negligible, but the Unruh effect on an inwardly falling observer becomes infinite. (why? no bounded acceleration can reach the speed of light, thus the acceleration must be unbounded). The Unruh radiation would cause an inwardly falling observer to evaporate, before the observer reaches the speed of light with respect to the Schwarzschild observer.
Which begs the question, can any quantum particles fall inside of their own event horizon? But that question will only be answered once some can come up with a Riesz Representation Theorem for Tensor Spaces.
Aaron, I'm winging this as a middle-brow in this topic, but: Unruh effect has to do with "acceleration" defined in terms of inertial physical standards (like, felt by a mass-and-spring accelerometer) rather than second derivative of coordinate motion per se. Hence a "falling" observer shouldn't experience an Unruh effect anyway, or at best something relating to the tidal fields (which, unlike base physical acceleration, are not transformed away by coordinate acceleration.)
ReplyDeleteAnyway, like I said the detection of "radiation" in these cases is relative to observer context (see my and Bee's exchange earlier.) Otherwise bystanders could in principle detect some other observer's "Unruh radiation" in their own, physically unaltered environment (especially by moving past her.)
One thing I still wonder about: if you approached a BH rapidly, then any "radiation" you perceived - including Hawking type - would be blue-shifted, which ought to have radical consequences as approach velocity nears c.
So your claim is that the acceleration of an inwardly falling observer is a consequence of the coordinate system (like choosing a rotating frame), that can be transformed away?
ReplyDeleteLast time I checked one could throw a test mass out back from an inwardly falling frame and then measure its acceleration. So while, at any given point the first derivative of the inwardly falling frame can be made to vanish, hence the inertial coordinate claim, one cannot make the second derivative vanish, regardless of the coordinates chosen. The point is, even a freely falling observer can conduct experiments in their rest frame to determine if their frame is accelerating, and I'm pretty sure that is the whole point of the equivalence principle.
The Unruh effect is because the momentum operators in an accelerated frame do no commute; precisely because the second derivative of the transformation is non-vanishing. Inwardly falling observers, like constantly accelerating observers have non-trivial vacuums.
What Hawking showed is that the vacuum is non-trivial for a Schwarzschild observer stationary at infinity, however the non-triviality is almost trivial.
But if you're "falling" there is no "gravity" in your reference frame, that is the whole point of weightlessness and saying that
ReplyDelete1. falling in a gravity field is roughly like having no gravity at all,
2. acceleration in inertial space is like having gravity.
Effects pertaining to "acceleration" are supposed to mean physically palpable acceleration. I don't know how that applies to Unruh effect, but REM that "falling" past an accelerating observer means just floating inertly in space, there can't be anything for that observer to find.
Ah, you are thinking about accelerating rocket ships: that force on springs and masses is due to the the engines transmitting the force (via VanDerWaals forces and other molecular effects) to you.
ReplyDeleteIn fact in an inwardly falling frame you could setup a clever experiment with a long spring and mass held in the direction of fall. Because force goes as inverse square of distance (in the classical regime), the spring would be extended to the point where the Hooke's Law force equals the difference in gravitational forces, note that this is not a test that requires detecting a radial symmetry in the metric.
Hi, I hope a question from a non-physicist is permitted. I read Bee's original post on the black hole information loss paradox that she linked to in this article. That post contained what seemed to me to be a pretty comprehensive list of possible solutions, and the nagging problems with each. But to my surprise I didn't see what I thought was the leading possible solution, Leonard Susskind's holographic principle. Was it there in a form I didn't recognize, or is it held in such low repute by working physicists that it didn't merit inclusion? I'd love a response from any of you experts in the field.
ReplyDeleteAaron: I did not "limit the curvature at the horizon to 0." For all black holes larger than say 10 times the Planck mass, the curvature at the horizon is very small (it drops with the 3rd power of mass over Planck mass).
ReplyDeleteIt is wrong that the acceleration of the infalling observer is infinite at Horizon crossing, and it is also wrong that the infalling observer sees an infinitely hot bath of particles. As Neil remarks, if the observer is freely falling he is by definition not accelerated. In any case, the particle production in the gravitational field is not caused by the gravitational force, but by the tidal force. (If the force is attractive on all particles, you can't pull apart two virtual particles in a constant background field.) Hope that helps. Best,
B.
This comment has been removed by the author.
ReplyDeleteSo if we say it is observer dependent does this mean we have to "be there" for us to observe particle decay plethora extended beyond the collision point(calorimeter evidenced) in time?
ReplyDeleteI assume this exists in nature so that the event is more or less correlated as to what exists in nature is produce for examination under LHC measures.
As far as I know the phenomenological relation is thought to be in microscopic conditions that allow us to surmise that the QGP "is a real thing?" Qui/Non?
Best,
Dear Bee,
ReplyDeleteIs the information paradox representable in this way?
Whether I throw into a black hole a 1 kilogram mass of hydrogen at near absolute zero of temperature or a 1 kilogram mass of high temperature plasma, the end result is the same.
-Arun
Gilesgoatboy: "I didn't see what I thought was the leading possible solution, Leonard Susskind's holographic principle."
ReplyDelete?? I posted the link to the "Elephant and the Event Horizon", and we had a considerable discussion of the holographic principle.
Dear Arun,
ReplyDeleteWith some qualifiers, yes. I suppose you're talking about the total energy being the same not the (rest)mass. And you should be clear that your mass doesn't radiate anything off when it falls in, but I suppose that's what you meant. Oh and keep in mind that your mass should be spheric symmetrically distributed around the black hole. If it's not the black hole can radiate off multipole moments it gains (no hair and all). Best,
B.
Plato: Please don't let yourself be confused by what Neil and Aaron where talking about. It is not a good idea trying to explain the Hawking effect with the Unruh effect, though unfortunately an explanation attempt that can often be found. Yes, what an observer sees depends on his state of motion. In particular an infalling observer will see something different than an observer who is stationary and outward accelerating (somewhat away from the horizon). Either way, what is most often talked about as "the Hawking radiation" is the flux to infinity, and that's for an observer at rest there. Best,
ReplyDeleteB.
Ha, what I really should have said is whether one throws an equal mass edition of Sean Carroll's book or Peter Woit's book into the blackhole the end result is the same.
ReplyDeleteDepending on whom you talk to, of course, in one case, no information has been lost :)
Agreed curvature goes as the third power or radius, but your other points conflict with the Rain metric for an in-falling frame.
ReplyDeleteAn in-falling observer who is by definition "not accelerating" will be in for a nasty surprise when confronted with the ground.
By that definition there would be no Unruh effect, because an observer that is freely falling in the Rindler metric would not be accelerating.
Speed is relative, but acceleration is not, it can always be detected. A freely falling observer can always compare his speed at t+delta to his speed at t.
Aaron: What of what I said disagrees with what? Could you be more explicit please? What I said was that freely falling is the GR generalization of no acceleration. The observer gets accelerated when he hits the ground, not when he falls. I did not say acceleration cannot be detected. There is no Unruh effect for a not-accelerated observer. Best,
ReplyDeleteB.
How does the ground know how far an observer has fallen from?
ReplyDeletehi bee, well I, for one, am not interested in this topic (or discussion)anymore(though I mentioned measurement process in connection with BH information loss problem). best,
ReplyDeletea
Thanks Bee,
ReplyDeleteMost certainly it requires some anchoring in reality that we could capture the essence of what is seen "in that moment" of the collision process to help to forwarding perspective into the expression of that particle decay.
Cerenkov radiation in ICE is a recognition of such a result. As well as, muon detection recorded in Gran Sasso
When an initial pure quantum state undergoes gravitational collapse to form a black hole, the final state at the end of black hole evaporation will always be a pure quantum state.
Stephen W. Hawking, Kip S. Thorne, John P. Preskill
Pasadena, California, 6 February 1997
The black hole Information Paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could "disappear" in a black hole. It is a contentious subject since it violates a commonly assumed tenet of science—that information cannot be destroyed. If it is true, then cause and effect become unrelated, and nothing science knows, not even our memories, can be trusted.
Parentani showed that the effects of the fluctuations of the metric (due to the in-going flux of energy at the horizon) on the out-going radiation led to a description of Hawking radiation similar to that obtained with analogue models. It would be interesting to develop the equivalent formalism for quantum analogue models and to investigate the different emerging approximate regimes.
On the Universality of the Hawking Effect by William G. Unruh and Ralf Schutzhold
Addressing the question of whether the Hawking effect depends on degrees of freedom at ultra-high (e.g., Planckian) energies/momenta, we propose three rather general conditions on these degrees of freedom under which the Hawking effect is reproduced to lowest order. As a generalization of Corley’s results, we present a rather general model based on non-linear dispersion relations satisfying these conditions together with a derivation of the Hawking effect for that model. However, we also demonstrate counter-examples, which do not appear to be unphysical or artificial, displaying strong deviations from Hawking’s result. Therefore, whether real black holes emit Hawking radiation remains an open question and could give non-trivial information about Planckian physics.
So looking for some correlative function for me was to move QGP forward "as an environment with which decay arises out of," one might consider the acoustic agenda with which phonon exploration has some relation?
It was closely related to the fluid dynamics(Navier- Stokes) with which this region could be calculated in terms of the viscosity, as well as it's relation to superfluids in the extreme. That relation is very important.
Because in it's cold/heat extremes, the correlation is equivalent as to what results in the location of the region of the singularity is not in the truest sense dense but very transformal of the pure quantum state? Leaves it's presence all around so no information is lost.
The bulk constituents then form the palette of experience of all that materialize in the entropic realization as relevant factors of information from that "super-symmetrical state?"
Best,
Overlap of "quantum" and "classical" behaviour
ReplyDeleteExplanations of Hawking radiation around a black hole often use a description of quantum-mechanical pair production effects occurring on a curved spacetime background. Although this paradigm does not obviously lend itself to a "classical" reinterpretation, research on the black hole membrane paradigm has revealed some overlap between "classical" and "quantum" descriptions.
"Analogue Gravity"
by Carlos Barceló and Stefano Liberati and Matt Visser
Abstract
Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity).
It is the "faster then light conditions" that reveal events at it's furthest reaches from the decay chain? These conditions had to be provided for in the collision process to be able discern results in ICECUBE or Gran Sasso? A pure quantum state had to be generated?
Best,
Just one last link here
ReplyDeleteThanks for your patience.
Aaron: The ground doesn't know how far an observer has fallen, it only knows the momentum at impact. Best,
ReplyDeleteB.
I was objecting to the comment that the observer only gets accelerated when they hit the ground.
ReplyDeleteIf the observer is freely falling, he is only accelerated when he hits the ground. That incidentally is why it's so unpleasant. Free fall is zero acceleration and qua equivalence principle locally the same as zero gravity. That's how zero G flights work. That's where Einstein got his insight from when he talked to the men who fell off the roof. I have no clue what your problem is. Best,
ReplyDeleteB.
GOCE delivering data for best gravity map ever
ReplyDeleteGravity is stronger closer to Earth, so GOCE was designed to orbit as low as possible while remaining stable as it flies through the fringes of our atmosphere. To help avoid drag and ensure that the gravity measurements are of true gravity, the satellite has to be kept stable in ‘free fall’. Any buffeting from residual air at this low altitude could potentially drown out the gravity data.
@Aaron Sheldon:
ReplyDeleteIn GR, at a sufficiently small region, a free-falling frame is equivalent to a inertial frame of SR. So an observer attached to a free-falling frame will not experience any acceleration.
In GR, objects free from the action of forces move in accordance with the curvature of spacetime (i.e. along geodesics). Gravity is not a force in GR, but simply the curvature of spacetime geometry.
Suppose an object A is fixed to the free-falling frame.
If another observer measures (in her frame) that object A is accelerating, and no external forces can be measured acting on the object, then this means that spacetime is curved because her geodesics is deviating from that of A.
If the object A crashes on the floor, what really happens is that a force (electromagnetic in nature) is applied to the body at a very short interval of time, quickly changing the momentum of that body. This very fast change of momentum ("impulse") is nothing less than a large deceleration, felt therefore as a collision.
Chris
hi bee, correction, this topic is indeed interesting. What is metric at the surface of BH?
ReplyDeletebest,
a
So an observer accelerating at 1G because of a rocket pack is different then an observe who has jumped out of an airplane and accelerates at 1G?
ReplyDeleteOr suppose the ground was soft and accelerated the observer at only 1G.
The point is that you can't negate the affect of second derivatives of the transformation in coordinates.
If observers in free fall about a gravitating body experienced no acceleration, then things like the precession of a rigid rod would not occur, nor would laser interferometry be able to resolve gravity waves.
Just consider this simple thought experiment from, quite literally any first year mechanics text book, usually around chapter six: a radially in falling observer has a spring and mass that moves along a rigid rod, the extension of the spring then depends on its orientation in space with respect to the gravitating body, longer pointing towards and away, neutral perpendicular. The rod, spring, and mass assembly is sensitive to the second derivative of the metric, or the curvature, or the acceleration, or the force. Taking the difference in readings of two such assemblies separated by a distance is the basic engineering of gradiometric tensometry, which is used by the US submarine fleet to map the ocean floor, and thus to aide in navigation.
If the object A crashes on the floor, what really happens is that a force (electromagnetic in nature) is applied to the body at a very short interval of time, quickly changing the momentum of that body.
ReplyDeleteI think it is more the exclusion principle in action and less the EM force. It is the exclusion principle that gives matter its extensive properties (e.g., volume is additive).
Anthony: A black hole has no surface and in any case the metric is coordinate dependent, thus I don't know what you mean with the question. Best,
ReplyDeleteB.
Aaron: If the observer is freely falling, he doesn't accelerate at 1G. I still don't know what your problem is. As Christine said, gravity is not a force, it's a property of space-time. You are still confusing acceleration with tidal force - that's the 2nd derivative, it scales like the curvature. That's exactly why I've told you way up the curvature on the black hole horizon is very weak. See a light on the horizon now? Best,
ReplyDeleteB.
Arun, Christine: My understanding was also that it's EM not the exclusion principle, now I'm confused. We're here on the level of molecules, not atoms. Thing is you can't push your body's molecules through those of granite without breaking bonds, but that's molecular binding what prevents you from doing that. You can very well push your way through air. Best,
ReplyDeleteB.
Arun and Bee:
ReplyDeleteSure, the exclusion principle explains why atoms occupy volume through the short-range effect of the repulsive exchange (spin-spin) interaction. This is additional to the long-range electrostatic or coulombic force.
Now if you have a large enough energy collision, I suppose that even the atomic structure could be disrupted and eventually you'd have to deal with "degeneracy pressure". You can estimate the energy for that. But ordinarily, the exclusion principle explains the existence of different chemical elements and their various chemical combinations, as well as a large number of mechanical properties of solids, including other properties such as electrical, magnetic and optical. With a low enough energy collisions, the EM interaction is at work at the level of molecular binding.
Christine
On the other hand, I suppose there is no energetic enough collision to lead a body into (a local or momentary) degeneracy pressure; I suppose such a condition can only happen inside white/neutron stars, since one needs a large gravitational force in order to reorganize the internal matter configuration and its stabilization under degeneracy pressure. A collision could disrupt atoms, but I'm not sure on the role of the exclusion principle after you have disrupted it.
ReplyDelete"after you have disrupted it." -> "after you have disrupted the atoms".
ReplyDeleteHmm, food for thought. The way I saw it is that why volume scales linearly with the number of particles N is because of the exclusion principle and not because of EM forces. In the absence of the exclusion principle the volume of a body would scale with number of particles as N^a where I believe the exponent a is less than 1. When I collide inelastically with the snowball thrown at me, if we were bosonic matter the snowball and I might coalesce into a something smaller than me and the snowball separately, regardless of molecular bonds.
ReplyDeleteBut I see the merit of what Christine says, so I have to think about it.
Molecular bonds are essentially due to the arrangements of electrons between atoms - they would not exist if all the electrons in each atom could sink to the 1s orbital.
ReplyDeleteArun,
ReplyDeleteSure, but when two bodies are getting closer and closer, i.e. when the most external orbitals/bands of the electrons of the atoms/molecules of the first body are closer and closer to those of the second body, the main mechanism in action is the electromagnetic repulsion of electrons in both bodies. The molecules or even atoms will be dissociated first than at the point in which any two electrons are "squeezed" together in order to occupy the same state in the atom (which, surely, they cannot).
So, it is true that the orbitals/bands are ultimately due to the Pauli exclusion principle, but the electromagnetic repulsion will come to operate much earlier by tearing appart the molecules of both bodies, including other ultimately mechanical effects such as transfer of kinetic energy into thermal, etc.
To get to the point of saying that a collison of two extended bodies is due to the Pauli principle, I guess one would have to show that the collision is energetic enough so that the electromagnetic repulsion between electrons plays no role in the sense that it is not enough to stop the electrons from moving towards each other at the point of forcing them to occupy the same state, or something of the sort. But I may be wrong, let me know whether my line of thought is flawed.
hi bee, I think I misunderstood something. What do you mean by singularity?
ReplyDeletethanks,
a
A singularity is where geodesics end at finite proper time and cannot be extended. (If such points exist the spacetime is said to be geodesically incomplete).
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteBee, I'm not sure this is the right place to post the following, but in any event, this just in this morning:
ReplyDeleteLubos Motl has tossed another log on his Verlinde stake-burning here. The paper it refers to was just released today by Nature Magazine by Holger Muller, Achim Peters, and Stephen Chu, "A precision measurement of the gravitational redshift by the interference of matter waves". Since I do not subscribe to Nature, I cannot read the paper. Do any subscribers to Nature here care to comment, before Lubos weighs in?
Stephen Chu ?! Isn't that the current US Secretary of Energy! What's he doing writing papers? Isn't he supposed to be dispensing funds for scientific projects and "energy" stuff like nuclear plants, solar panels, etc.?
Steven: Sorry, Busybee currently has no time to read the paper. If colyersteven at yahoo dot com is your email address, go check it. Best,
ReplyDeleteB.
I did check it and thank you, Bee.
ReplyDeleteI have just one needling point to clear up, sorry.
Bryan said, 5th post from the top: But if the microstates of a black hole are described using classical parameters like momentum, charge and mass, then there doesn't seem to exist a non-trivial set of microstates at all.
Excuse me if I'm wrong, but shouldn't "momentum" be replaced with "spin"? I understand spin is tied in somehow with angular momentum, but is calling it "momentum" acceptable?
You're welcome. I believe he meant angular momentum. (The black hole can have a momentum, but it's usually considered in the restframe.)
ReplyDeleteWouldn't angular momentum be degenerate?
ReplyDeleteI understand that Spin and Angular Momentum are inter-related but I also understand they are two separate things.
ReplyDeleteLove your "rest frame" comment. Spoken like a true Theorist. I also understand your comment about Momentum, as in Linear Momentum. Indeed, I'm trying to think of a single thing in our Universe that doesn't have it. The best I can come up with is "rest frame" in the mind of a Theorist, possibly nowhere else.
Ah, I just found the source of my confusion, a single paragraph in Carroll's "From Eternity to Here" that confuses spin and a.m.
So, complete the following sentence (multiple choice):
A black hole is uniquely defined by mass, charge, and ...
a) spin
b) angular momentum
“The evolution laws in quantum mechanics are time-reversal invariant. (That does not include the measurement process, which does set limits to our knowledge).”
ReplyDeleteFrom your earlier post: Backreaction: The Black Hole Information Loss Paradox
I am surprised to learn that quantum mechanics is so comfortably deterministic and that only our queries of it (measurement) are uncertain and probabilistic.
I think I misunderstand or that perhaps this is a philosophical black hole, best to be avoided.
Thanks for your posts.
To our best present knowledge, it is as I stated. You can find that in any textbook on quantum mechanics. It is not so much the queries that are uncertain, but rather their outcome. I on my side are surprised you don't know that. Makes me feel like my writing sometimes is actually good for something :-) Best,
ReplyDeleteB.
"It ain't what you don't know that gets you into trouble. It's what you know for sure that just ain't so."
ReplyDelete-- Mark Twain
I think I have more trouble with what I don’t know.
Be that as it may, in relation to the notion of information, are objects in quantum mechanics (an electron, say) thought to exist continuously or are they continuously “refreshed” by some internal dynamic? That is, is information seen as a constraint on possible dynamics?
My apologies if there are no solid handles in this question.
Thank you.
In the standard framework they exist continuously.
ReplyDeleteI may well be out of bounds here, trying to project a simpleminded mythos into a domain where such things are properly excluded, persisting in a need to explain nature as some grand interplay of elemental protagonists, but…
ReplyDeleteWithin the standard model is there any implicit sense of information as an active agency, something that affects outcomes, a counterpoise to energy? Or is information simply an adamantine attribute, passively passed along? For that matter, is there any place for active agency in QM, are there verbs as well as nouns? Does energy have juice or is it simply the projection of some dry underlying geometry?
Surely, if these questions are beyond rescue, you will allow them to bob on downstream.
Regards.
Don,
ReplyDeleteThere is no notion of active or passive agency in physics. There's theories, mathematical models, that are experimentally tested and describe the world to a certain accuracy. Elements of these theories can have certain properties assigned to them. Energy and information can be among them. It depends on the theory you work with whether these are well-defined and thus meaningful and useful. I frankly have no clue what your question means, can you be somewhat clearer? Best,
B.
I thank you for your courtesy here and, within Niels Bohr’s recommended limits, there is a possibility that I can be clearer.
ReplyDeleteWith regard to the notion of information, it seem likely we could do with a few more words to discriminate among it’s various species. For example, Shannon’s communication engineer would not consider information to be a conserved property, but that is not the issue here and I understand the apparent need for information to be conserved in QM.
It may be that I am trying to project a general system’s view onto physics and finding that it does not fit on any single page. Perhaps it is implicit there, simply veiled in detail. And perhaps it is simply erroneous, properly excluded.
Consider that Scott Russell first observed the solitary wave from horseback, and yet, it has been found to have dynamic analogues in various physical contexts at scales across a great many orders of magnitude. Furthermore, we may observe that loosely periodic phenomena are rife in the universe with phases varying over thirty orders of magnitude.
Is there some general overarching principle at work here, does it reveal an elemental interplay in nature? If so, is it formalized in physics proper or does it have any utility there?
Once again, if these questions are both too little and too much, rest easy in allowing them pass on by.
Regards.
Don: I am sorry but I genuinely have no clue what your question is. I'll just leave it standing, maybe somebody else has a reply for you. Best,
ReplyDeleteB.