jana

Whatever.

I used the word "enormous" to highlight the fact that I wasn't talking about microscopic holes. The point is that as a hole increases in mass as we go to the ultraviolet, it's exterior goes to the infrared and is therefore described by effective field theory with increasingly good accuracy. In other words, unlike in nongravitational physics where large energies probe short distances, the formation of large black holes as a result of collisions between sufficiently high energy objects means that large energies instead probe the long distances characterizing the region exterior to the hole. This is one aspect of the UV/IR connection I want to discuss. So are you going to answer any of my questions straight up, or are you going to continue with your conspicuously odd (and that is putting it charitably) behaviour?

For example, the schwarzshild radius is R=2GM, so large mass means large hole.

I’ll try, but we should also get into the habit of giving more than just citations. I’m sure you’ll agree that these forums are meant more for conversation than bibliographies. What we’re after is a microscopic picture of black holes that macroscopically reproduces the black hole area-entropy relation. The crucial question is; does the entropy in this formula arise from the contribution of all degrees of freedom of black holes (I inferred from this paper that this is the majority view), or only those associated with their event horizons? Let’s look at LQG first. It’s easy to make a guess about how things must work in LQG. Since according to hawking-bekenstein, black hole entropy is area-extensive, only area-extensive degrees of freedom can contribute, and these of course are given by spin-network links puncturing surfaces. It is also obvious that this surface must be the event horizon since what other surface could possibly give the hawking-bekenstein relation? Given these two assumptions, we don’t even have to perform any calculation to see that the resulting entropy will be in the macroscopic limit proportional to the event horizon area. Unfortunately it is also clear that this calculation can’t on it’s own determine the constant of proportionality, which gives cause to be dubious about LQG since a correct non—perturbative QG theory should be able to provide us with this without the need to resort to external arguments. Thus LQG must take the (less popular) view that black hole entropy arises only from degrees of freedom associated with event horizons. So far this is just mathematical handwaving in the form of dimensional analysis. What we need is the kind of aforementioned additional physical argument to justify this mathematical one. The sorts of arguments used to do this are actually statistical-thermodynamical. For example, carlo rovelli considers in this paper the thermodynamical behavior of a system containing a schwartzshild black holes and simply notes that their behavior cannot be affected by their interior degrees of freedom. Naively, this intuitive argument makes the majority view seem absurd. Yet not only does the string argument in this paper yield this view, it gives precisely the hawking-bekenstein relation, correct coefficient and all! I don’t understand the details of the argument, but I’ll say what I do know. The hard part of the argument, which I don’t understand, is the construction of black holes from D-branes. The entropy is obtained using the representations theory of D-branes which allow one to determine the total number of states of the black hole by explicitly counting them. On the other hand, completely independent of this, we can compute the hawking-bekenstein entropy from the mass and charge of the hole vis a vis the masses and charges of the individual constituent D-branes. On comparing these two very different calculations we find, seemingly miraculously, that they agree. Note that unlike with LQG, it appears that there is no need for appeal to independent arguments to produce the correct result. I must say that I’ve found it quite difficult to remain unmoved by all of this. As you alluded to, the D-brane calculation only works for extremal and near-extremal holes. The latter category is important because it means that there is every reason to believe that the result will survive the breaking of supersymmetry, if we ever find a way to do so. But unlike string theory, all of the degrees of freedom of LQG have been identified so one cannot expect some new constant to suddenly appear within it. So if you believe, as I suppose most probably do, that the correct QG theory should be able to produce the hawking-bekenstein relation in toto, and that the majority view that hawking-beckenstein entropy accounts for all degrees of freedom is true, you should be worried about LQG. This sounds almost like an insult. Just assume I won't believe you understand anything you say unless you explain things in your own words.

I believe that the LQG derivation of the proportionality between black hole entropy and area (there appears to be no way in LQG to obtain the coefficient of this proportionality) is invalid since instead of treating complete black holes, microstates of area of their event horizons are counted as if black hole interiors don’t even exist and with no justification that I can see given for identifying these microstates with the fundamental states of black holes themselves. This seems to yield the expected proportionality trivially, as a cheat, their argument in effect assuming the entropy-area proportionality it is suppose to prove. On the other hand, the string demonstration appears to honestly build entire black holes out of D-branes and then counts their true physical states, the result being in complete agreement with the standard formula. One more thing. I now feel that the criticism levelled by LQG people at string theory to the effect that it “only proves this result for extremal and near-extremal black holes” really misses the point, this being that for strings to be correct requires that they at least produce the correct result in every situation in which this calculation can be carried out, and so far it clearly has. Moving on, were you aware that, according to this recent paper, it is in fact not known for sure whether LQG is in fact a description of quantum geometry that is truely background-independent and discrete? I’m going to think about this for a little bit before posting anymore about it.

Okay, but the black holes I've been discussing are of transplanckian mass and thus enormous. Martin made an understandable mistake when he entitled the thread "...microscopic black holes..."

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That's okay since I'm really just trying to reevaluate my own attitudes, and I'm finding bouncing this stuff off of you helps. These next arguments I’ve been reading about require that we consider background-independence in the very general context (e.g., more general than LQG) of the wilsonian RG for QFT. In this framework, the true fundamental degrees of freedom occur at some very high energy represented by an ultraviolet fixed point of the RG beta function defined as usual on coupling constant space. The points along each possible trajectory traced out by the beta function as we move from the ultraviolet to progressively lower energies represent increasingly course-grained approximations of the fixed point theory, eventually reaching in the infrared the various endpoints of each RG flow representing some vacuum or background. In these terms, background-independence means insensitivity of the fixed point theory at high energies to the different possible vacuums at low energies. This is known as “short-distance universality” or just “universality”. For example, LQG is hoped to be an ultraviolet fixed point which flows in the infrared to classical spacetimes whose dynamics is governed by GR. Notice the clean separation between the expression of background-independence here and the idea of relationalism it is somewhat conflated with when discussed in the context of GR. In fact, GR doesn’t come up at all here! As another example, string theorists have believed that all physically admissable backgrounds flow in the ultraviolet to a unique theory at high energy called M-theory which would thus be background-independent. It would then only remain to discover it’s degrees of freedom and precise form. In this case, the question is whether and how the conventional meanings and implications of RG notions like fixed points and flows extend beyond the paradigm of field theory to whatever new paradigm M-theory represents. In fact the argument I studied says that there can be no background-independent QG theories since the (conjectural) domination in quantum gravity of transplanckian scattering processes by the production of correspondingly extremely massive and hence very large black holes (tom banks calls this conjecture “asymptotic darkness”) ruins universality. The idea is simply that asymptotic darkness means that transplanckian scattering instead of probing short distances, instead probes distances of order the size of these very large black holes. The resulting entwining of large scale geometry with the high energy spectrum means that the fundamental degrees of freedom depend on vacuum dynamics thus preventing background-independence. This is an example of the celebrated but still mysterious “UV/IR connection” which is yet another idea intimately related to holography. We conclude from this that in general, different backgrounds correspond to different QG theories so that the aforementioned traditional view that string theory gives rise to a unique QG theory called M-theory is wrong, though this doesn’t mean that string theory is wrong. It goes without saying of course that this isn’t a happy argument from the perspective of the nonstring nonperturbative QG crowd. In my next post I'll discuss a troubling aspect of the LQG black-hole area-entropy argument, and also from a point of view different from the above the claim that LQG is a background-independent and discrete theory of spacetime.

Yes, it is conjectural; we have arguments but no proof. But I'm trying to psyche myself up for the deep waters of string theory. I need more than mere logical possiblility (e.g., for whatever reasons, "I reserve the right to believe in LQG or anything else until I'm shown an airtight proof that it is wrong"). I need believability, and so far, I find these black hole arguments to be quite plausible. In fact I know that they are taken seriously by many (in fact my impression is most) people. Of course there are probably many subtleties that I'm completely missing (maybe I'm missing the boat entirely, which would of course suck greatly). Before I spew out what I learned in relation to all this about background independence, I'll say one more thing. In quantum gravity the measuring apparatus is always coupled gravitationally to the system. This suggets that the only sensible way to define observables in quantum gravity is with respect to measuring apparatus placed at asymptotic infinity. This means that defining quantum gravity is problematic for spacetimes that don't have appropriate asymptotic properties. The point is that it may be that the only observables allowed in quantum gravity are those whose data lives on the boundary at infinity (for spacetimes that have boundaries). In other words, the only sensible observable would be the S-matrix, and this is consistent with holography. This is the case with string theory, but in LQG, area and volume operators serve as fundamental observables. So my next post will be about background-independence. I’ll relate as best I can an argument based on this black hole stuff that suggests that there is no such thing as a background-independent theory of quantum gravity, and in particular, that the idea that M-theory can ever be background-independent is wrong.

I moved this post to the microscopic black holes thread

Hi martin, are you familiar with the fairly basic and widely held belief that in any quantum theory of gravity, scattering at transplanckian energies will most probably be dominated by black hole production?

What is the basis for your "suspicion"?

Actually, that was an incredibly sporting thing to do, so thankyou very much! But although I'm studying very hard, what I say should be checked carefully since I'm only an undergraduate and make mistakes all the time.

Thanks.

I believe you are referring to "braneworld" scenarios. The idea is that the universe consists of three dimensional slabs, called branes (short for membranes) embedded within a higher dimensional space. We live on one of these slabs. The idea is that these branes interact with the higher dimensions and each other only gravitationally, with all other interactions (electromagnetic, strong, weak) restricted to individual branes. The weakness of gravity compared to the other interactions is then a consequence of this.