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Dear Lubos
Thanks for the nice review. I have a couple of clarifying points:
1) we don't actually make any conclusions about Bousso-Polchinski, where disorder (if present) is asymmetric (rates of tunneling upwards and downwards are not equal in the average). We consider tunnelings between KS throats on multithroat CY. However, I would expect that the result holds for disordered BP landscape as well.
However, the source of disorder on BP is unclear for me at this point.
2) time is a world time of 4d observer
living on the D3 brane tunneling between the throats
3) we don't actually cite Sarangi-Shiu-Shlaer because the guys themselves did not consider their work related to ours, according to their email. We do cite papers by Henry however.
With best regards,
Dmitry.
Dear Dmitry, thanks for this amazingly speedy and clarifying visit.
1) I would see no problem if the BP landscape had no disorders. You don't have to apply globally, after all, do you? 
2) Does it matter whether the observer on the D3-brane is moving, whether you measure the time in 4D Planck units or 10D Planck units or something else, and what happens with the time if the D3-brane collides with the throats etc.?
If the time were a "universal" time for a wavefunction of the Universe, I would understand it better but why should some subjective proper time measured by a particular observer at a ten-dimensionally generic point of the compactification have such a fundamental impact on the evolution?
3) Oh, you are right, you do mention the 0708 paper by Henry Tye. I had to do my search in an incomplete way. Yes, Tye is surely closer to your work. It was just the chronological bias that made me consider these two papers simultaneously - they were published (almost) on the same day.
All the best & good luck
Lubos
Haloscan.com: The following comment has been automatically labeled as nonsense. We apologize for any inconvenience.
The finding the string landscape solution in distribution of random fluctuations is nothing very new from Aether Wave Theory perspective, where the strings corresponds the foamy density fluctuations inside of dense particle environment, which is created by the same way by recursive way.
...I see, just a some Matrix error..
Dear Lubos
One does need disorder to get Anderson localization. In the absence of disorder, maybe some vacua on BP are dynamically preferable (for sure, the ones with small number of fluxes are, since transition downwards is always more probable), but this fact is not related to Anderson localization and the number of independent tunneling directions.
As for the choice of time - the question, I think, is more what is P 
If P is the probability to measure a given value of the cosmological constant in a given 4d Hubble patch, then tau is the world time of 4d observer. Of course, you can choose different units to measure it, but this choice will also rescale correspondingly the tunneling rates (probabilities to tunnel per unit time).
What happens with time when D3 brane collides with the throat? I think nothing special happens, just new inflationary stage starts, with effective inflaton being the distance between the D3 brane and the tip of the throat.
Cheers,
Dmitry.
Dear Dmitry,
I think your first point is appreciated on my side. Anderson localization is not automatic, it just happens when you have the appropriate strong impurities there and it becomes easier if the effective dimension of the space is small. And there are other effects influencing the dynamics including the asymmetry of the tunneling rates.
But it is still difficult for me to follow the sentence "If P is the probability to measure a given value of the cosmological constant in a given 4d Hubble patch". Why?
Because if one considers a "given" 4D Hubble patch, it should already have a well-defined i.e. "given" curvature, shouldn't it? What does it mean to have a "given" patch whose curvature (and volume and radius) are uncertain i.e. "non-given"? It sounds like a letter from a car shop saying "once we *give* you a car for your money, there is some probability that you will actually receive the car and some probability that it will be a Trabant." That's not how I imagine giving a car, especially after they were given the money. This comment of mine may sound as a silly game with words.
Except that I think that the uncertainty hiding in the definition of "given" and "probability" includes an uncertain factor of the Hubble volume and similar factors that lead to ramification of various anthropic papers. Are you claiming that you can settle these questions and decide whether your P should be proportional to the Hubble volume in Planck units or not? What are the rules that decide about the presence of the volume factor here?
If you talk about probability distributions for a property of the Universe, it should be operationally defined as the fraction in a certain ensemble of (different) Universes (with different vacuum energies), p1=N1/N, so I don't quite follow how you can associate this probability with one "given" Hubble patch. Sorry if I am unclear.
Concerning the last point, sure, I understand that you get inflation but my real question is what happens with the probability distribution if the inflationary era begins. This question is related to the previous one because inflation will lead to an exponential increase of various volumes so I wonder whether this will make the states with D3 branes deeply immersed in the throats much (exponentially?) more likely or not. It is still about the way how the Hubble volume and related quantities influence the "probability" of having various values of Lambda. It seems that there is no unity among the researchers on similar issues and so far I tend to think that no justifiable method to settle this huge uncertainty is known.
Best & thanks
Lubos
Maybe my imagination is going a bit haywire here, but it seems like the cooling tower's hyperbolic shape is symbolic of a de Sitter universe expanding hyperbolically...
She's brought sexy back.
Seeing these two pics together I can't help but be reminded of Larry R.'s comment about how a woman's cooling tower acts as a warming device for him.
"(...regardless of the precise justification of their special role simply because) special things deserve a special treatment"
If it isn't already, that should probably be some kind of Natural Law. How would that equation look?
RA, I'm intrigued. Do you have a link for the comment?
Pardon, Cynthia.
Aaron, pardon me, pardon me about what?
Dear Lubos
Thanks for keep asking interesting and physically important questions
Since the answer had to include technicalities (formulae inparticular, and Wordpress works with them so much better than the Blogger), I answered on my blog here:
http://www.nonequilibrium.net/to...-in-particular/
Cheers,
Dmitry.
Dear Dmitry,
thanks so much. First, I am always jealous about the LaTeX capabilities of other systems but so far it was possible to survive the jealousy without any transfers of the website.
So if I understand well, your degree of freedom is really the inflaton phi, and it is one degree of freedom per Hubble patch, with one expectation value and one variation. The value of the inflaton is assumed to directly control the Hubble constant and the size of the patch, according to the normal equations.
So you neglect all higher-frequency modes of the inflaton and other fields which may or may not be a sane truncation. Moreover, when you create new causally disconnected bubbles, you probably suddenly increase the number of degrees of freedom of the system, with a new phi per every new patch, don't you? Such sudden jumps indicate that the original truncation was probably not 100% fair, was it?
OK, let me accept it. It is some sort of minisuperspace approximation. Then, it seems that your answer about the volume factors is a resounding No. If the Hubble radius (and patch) is large, it doesn't make its value of the cosmological constant more likely. It is still some value of the inflaton, one observable which is the only degree of freedom, right? For the same reason, one doesn't increase the probability of D3-branes deep inside throats. Isn't it a prediction that inflation shouldn't occur then?
The "funny thing" you are describing is the traditional freezing of the quantum fluctuations, or something else? Strictly, is it OK to assume that such a process is microscopically a result of decoherence? I am confused about various additional kinds of tools, including superHubble fluctuations.
Those of us who tend to believe complementarity think that these modes don't really exist because all the information behind the horizon is a scrambled gauge copy of the information inside the horizon (of course, it can be a scrambled copy of some degrees of freedom you omitted), much like in the black hole case. Is that OK to conclude that your picture assumes/implies that complementarity can't hold?
Sorry if I increased the confusion. I think you have given me answers to all my questions. The only issue is whether I (already?) fully believe them.
Good luck, Lubos
For the link to the comment you referred to.
I meant to address you, but mis-read and addressed Rae Ann instead.
What is the comment from Larry?
Thanks.
Hi Lubots.
I guess yocould already know it and simply you don´t like it. But the idea is that you can have LaTeX in any website throught an external webserver, such as mymetex.
You can read all the info here:
http://www.forkosh.com/mimetex.html
In particular you should read the botton of the page, where it talks about the public mimetex server.
best regards.
LM: I've been using about 4 LaTeX implementations on this blog, including mimetex, Techexplorer, and (recently) a javascript LaTeX2html automatic conversion, but I removed all of them from the template because they are other slowing the website down or require special software or depend on servers etc. I don't need it that much.
L: So if I understand well, your degree of freedom is really the inflaton phi, and it is one degree of freedom per Hubble patch, with one expectation value and one variation. The value of the inflaton is assumed to directly control the Hubble constant and the size of the patch, according to the normal equations.
D: Yes, I am sure you understood me correctly. What I do is the following: taken a given Hubble patch, I focus only on the dynamics of IR degrees of freedom, that is, the ones with wavelength [tex] lambda > 1/(aH)[/tex] (so that I introduce a coarsegraining). Why can one do this? Physics at superhubble scales may be causally connected during inflation - both particle and event horizons in the de Sitter universe are exponentially larger than [tex]H^{-1}[/tex]: [tex]l_{rm horizon} sim H^{-1} exp (Ht)[/tex].
After the end of inflation one causally connected patch has the characteristic size [tex]H^{-1}[/tex], that's where the notion of Hubble patches actually comes from.
L: So you neglect all higher-frequency modes of the inflaton and other fields which may or may not be a sane truncation.
D: There are two things here: a) I care only about light fields (more or less with [tex]m
Dear Lubos
It looks like Haloscan does not accept too long comments I posted the full reply on my blog.
Cheers,
Dmitry.
I'll try to put here the whole text in two installations
D: There are two things here: a) I care only about light fields (more or less with [tex]m
L: Such sudden jumps indicate that the original truncation was probably not 100% fair, was it?
D: It is unfare in the same sense as description in terms of kinetic equation (or Fokker-Planck) is unfare compared to full QFT description. So, pretty much fare as long as you understand what you are doing (say, you are not interested in exponentially small corrections to the distribution function )
L: OK, let me accept it. It is some sort of minisuperspace approximation.
D: In fact, it is. You may not know it, but Hartle-Hawking wave function is the [tex]ttoinfty[/tex] asymptotics of the probability distribution - solution of the Fokker-Planck equation I was talking about last time.
L: Then, it seems that your answer about the volume factors is a resounding No. If the Hubble radius (and patch) is large, it doesn't make its value of the cosmological constant more likely. It is still some value of the inflaton, one observable which is the only degree of freedom, right? For the same reason, one doesn't increase the probability of D3-branes deep inside throats. Isn't it a prediction that inflation shouldn't occur then?
D: No, as you can easily see by introducing a model with [tex]V= V_0 + m^2 phi^2[/tex]. In the limit [tex]tto infty[/tex] there will be a distribution of effective cosmological constant values among the Hubble patches given by your favorite Hartle-Hawking wavefunction , but inflation will continue to run in each patch.
If one takes chaotic inflationary model, where inflation is actually allowed to end, then the probability for inflation to end is finite (say, one can calculate such things as the average number of efoldings which is not divergent).
L: So you neglect all higher-frequency modes of the inflaton and other fields which may or may not be a sane truncation.
D: There are two things here: a) I care only about light fields (more or less with [tex]m
Lubos, sorry for making a mess. Somehow Blogger also wants to cut my comments.
Cheers
Dear Dmitry, the limit for one (premium account) Haloscan comment here is 10 kB and it is unlikely that you broke through it.
A more likely reason was your attempt to squeeze some unusual TeX-like HTML into it? Thanks for the answers at any rate, I will read them later in detail.
Dear Dmitry, it was very helpful, thanks! You taught me some things I should have organized in my skull before. Yes, I think you have justified and bounded the validity of your approximation etc.
In the future, I will try to avoid similar errors as misidentifying the horizon size during inflation etc.
Even though I obviously think the same thing as you do about the ultimate success or failure of dS/CFT, it's the latter, your duality between Jesus Christ and complementarity is not quite clear to me. In fact, I don't even see any real link between complementarity and dS/CFT.
In my opinion, complementarity, at least in the black hole case, is a rather obvious qualitative feature of information in the black hole background. You can find slices through spacetime of an evaporating black hole at which you cross most of the Hawking radiation as well as most of the matter inside.
There seems to be a doubled information on the slice, and a natural answer apparently needed to avoid a quantum xerox is to say that the two copies of the information are not really independent. In fact, I don't think that this argument has anything to do with string theory.
Because GR dictates that event horizons in any context should have similar properties, it is natural to extrapolate such a principle of complementarity, to dS, too.
Dear Lubos, great blog!
I have a small problem with a recent paper from Ted Jacobson ( http://arxiv.org/abs/0804.2720 ). He argues:
"So it appears that the
only way to save black hole thermodynamics is to reject
the sort of Lorentz violation considered here (and likely
any other sort involving Lorentz violating dispersion)"
As far as I know some string theory based models propose a frequency dependent dispersion of light rays ( http://arxiv.org/abs/hep-ph/0605326 ). Does that mean (if Jacobson is right) that black holes with horizons cannot exist. Or does this kind of Lorentz symmetry violation have nothing to do with the one in T.J paper ?
Thanks if you answer and sorry that I interrupt your discussion.
LM: Thanks for the interesting topic. It is not right to say that string theory predicts any nonrelativistic dispersion relations.
It is only some physicists who vaguely use some tools and terms that also appear in string theory - such as the cosmic rays paper you mentioned - but string theory as found in textbooks and key papers implies that Lorentz symmetry holds.
It is very interesting if one can prove that the symmetry must hold by a consistency constraint involving horizons and the 2nd law. I must read the paper in much more detail than so far.
Update: I've read it and it is not new. They rely on work by Sergei Dubovsky etc. I have talked to Sergei about it many times and know it. It is OK. It is just being said that in a Lorentz-violating theory, different fields have different maximum speeds and thus different positions of the event horizons with different Hawking temperatures, and one can do unusual things in between them. But the gravitational field event horizon is always the outer one because gravity is the fastest - in consistent models of spontaneous Lorentz breaking such as the B-field etc.
Hi Lubos
Please don't take my jokes on religion-physics interplay too seriously
Thanks for the explanation of the meaning of complimentarity. Would you say that it holds only for spacetimes with event horizons? Does it hold in the presence of apparent horizons as well?
For example, suppose I am observer in Minkowski space living in the rocket. I than turn on the engine and start moving with acceleration. In my accelerated reference frame there is an apparent horizon and I feel thermal radiation from it. Is there doubling of information somewhere in this setup?
Cheers,
Dmitry.
Dear Dmitry, I try to take jokes both as jokes as well as potential inspirations for serious thoughts. Sometimes people tend to laugh at someone, pretending that it is obvious what they should think, but it is often far from obvious.
Various comparisons with religion may have some meaningful core but many other aspects of such analogies could be wrong. And vice versa. These analogies could be laughable in average but many aspects could still be legitimate.
Whether complementarity applies to the apparent horizons? Well, that's a great question. It must apply to some different horizons than the canonical event horizons - because an evaporating black hole doesn't really have the event horizon - but because I don't know the exact algorithm saying how the different regional degrees of freedom depend on each other, I also can't tell you which horizons had to exist for the overlapping effect to be nonzero.
If someone knows everything, she will surely also answer all of our questions.
I agree that there should be no doubling in your example constructed to have no doubling. But the absence of the phenomenon here might be related to your inability to sustain the acceleration for an arbitrarily long time. The fact that you can't have enough fuel to sustain the acceleration for too long is a part of holography, I feel - too much fuel creates another black hole, too.
"For example, suppose I am observer in Minkowski space living in the rocket. I than turn on the engine and start moving with acceleration. In my accelerated reference frame there is an apparent horizon and I feel thermal radiation from it. Is there doubling of information somewhere in this setup?"
This leads into another interesting question that is loosely connected. Apparently, there is still some debate about whether the internal temperature of an object moving at relativistic speeds increases or decreases.
http://arxiv.org/pdf/physics/9610016.pdf
http://www.mdpi.org/entropy/pape...rs/
e9030113.pdf
This question is somewhat interesting. In a purely empty space, one might be able to claim that there is no forced heating for an object moving at relativistic speeds, however, we do not live in empty space. Our space is filled with CMB and the reality is that for macroscopic objects, we must consider the heating encountered as we pass through space.
Any macroscopic object moving through space at high relativistic speeds will experience an extreme temperature gradient. With forced heating on the forward face, and near absolute zero temperature on the back face.
Again this is merely due to CMB, and is not the same as what would be observed by an independent observer who was watching the same object travel in empty space.
In a purely empty space, the same object would not experience any local heating, and if the object had an internal temperature, an observer would see that temperature blue or red shifting depending on the relative angle.
In a sense, one could argue that the CMB provides an absolute timing signal between all objects in the universe. An absolute temperature that must be shared by all (with some small deviations).
