AdS/CFT as quantum to classical correspondence


by naturale
Tags: ads/cft, kaluza-klein, quantization
naturale
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#1
Jan31-13, 05:27 AM
P: 104
This paper proposes an intuitive interpretation of basic aspects of Maldacena's conjecture in QFT and of the mathematical beauty of extra-dimensional theories. Its ansatz is that every particle is a reference clock. It is a peer-reviewed paper and uses an extremely original and simple formalism. Please discussed the paper in a fair and objective way.


Classical geometry to quantum behavior correspondence in a Virtual Extra Dimension


Donatello Dolce

In the Lorentz invariant formalism of compact space-time dimensions the assumption of periodic boundary conditions represents a consistent semi-classical quantization condition for relativistic fields. In [arXiv:0903.3680] we have shown, for instance, that the ordinary Feynman path integral is obtained from the interference between the classical paths with different winding numbers associated with the cyclic dynamics of the field solutions. By means of the boundary conditions, the kinematics information of interactions can be encoded on the relativistic geometrodynamics of the boundary [arXiv:1110.0315]. Furthermore, such a purely four-dimensional theory is manifestly dual to an extra-dimensional field theory. The resulting correspondence between extra-dimensional geometrodynamics and ordinary quantum behavior can be interpreted in terms of AdS/CFT correspondence. By applying this approach to a simple Quark-Gluon-Plasma freeze-out model we obtain fundamental analogies with basic aspects of AdS/QCD phenomenology.

Subjects: High Energy Physics - Theory (hep-th); High Energy Physics - Phenomenology (hep-ph)

Journal reference: Annals of Physics, Volume 327, Issue 9, September 2012, pp 2354-2387

http://arxiv.org/abs/1110.0316
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naturale
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#2
Feb1-13, 04:54 PM
P: 104
This paper is a Copernican revolution in physics . After more than 10 years it gives the formal prove of AdS/CFT, equ.(66), from clock periodicities. Must be read and understood.
mitchell porter
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#3
Feb2-13, 05:55 AM
P: 747
Are you the author?

naturale
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#4
Feb2-13, 06:17 AM
P: 104

AdS/CFT as quantum to classical correspondence


Quote Quote by mitchell porter View Post
Are you the author?
No. I'm not the author.

"Any intelligent fool can make things bigger, more complex, and more violent. It takes a touch of genius - and a lot of courage - to move in the opposite direction" A. Einstein
mitchell porter
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#5
Feb2-13, 06:18 AM
P: 747
Why do you have such confidence in the correctness of his work?
naturale
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#6
Feb2-13, 06:23 AM
P: 104
Quote Quote by mitchell porter View Post
Why do you have such confidence in the correctness of his work?
I read papers, it is published on a peer-reviewed journal, it is an intriguing idea. Why don't you read the paper and see if you can get the same conclusions?
mitchell porter
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#7
Feb2-13, 07:08 AM
P: 747
It seems that Dolce's big idea has nothing to do with AdS/CFT. He seems to be claiming that quantum mechanics is a manifestation of a compact timelike direction. That is, some time "t" in the future is literally the same as a time "0" in the past; space-time joins up with itself like a donut in which one of the cyclic directions is timelike. Quantum mechanics is to result from imposing these timelike periodic boundary conditions on a classical theory.

But then he talks about individual particles having individual internal times, with the time to repetition depending on the mass. I do not see how to make sense of this. Consider a particle that is created at one point in space, travels through it, and then gets absorbed somewhere else. There's no time loop, so what is the meaning of the "compact internal time" here? The original idea is to take repetitive behavior, like the cycling of the phase factor in an energy eigenstate, and to interpret it the successive cycles as literally identical: the next cycle doesn't just repeat the previous cycle, it is the same thing, because space-time loops back on itself. That might make sense if it was done on a single global scale, like a Godel universe, but how can you apply this interpretation to an object which is clearly created at one time and destroyed at a later time?

Regarding AdS/CFT, he only engages with it superficially. AdS/CFT is an identity of two quantum theories, a correspondence between a quantum string theory in AdS space and a quantum CFT on the boundary of that space. There are lesser versions of the correspondence in which you only concern yourself with a classical limit of the AdS theory, and he seems to be talking about that, and then trying to relate it to his earlier ideas about repeating time. I assure you that there is no proof of AdS/CFT here (and certainly no real discussion of either of the quantum theories in the duality), just some elementary talk about classical boundary conditions in AdS, that are combined in a confusing way with the already confusing ideas about cyclic time.

Quite a few people have tried to get QM from time loops. A few others hope to get quantum mechanics emerging along with gravity and the extra dimension, in an extended version of holographic duality. There are time loops in some versions of AdS. So it would be really interesting if you could indeed get QM on the boundary from time loops in a classical AdS bulk.

But I don't see anything like that here. I suppose it's obvious that I struggle to make sense of the paper, and that I think it is based on conceptual confusions that are hard to track down because they are never explicitly stated and rigorously defined, instead they are spread throughout the text as background assumptions. Maybe I'm missing something and it all makes sense somehow, but really, I doubt it. I have tried at least to pull out some of the component ideas which make sense by themselves, and to indicate how they might have been combined into a comprehensible research program, but I do not think that program is what Dolce is following, he's doing some other confused thing.
naturale
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#8
Feb2-13, 08:03 AM
P: 104
Quote Quote by mitchell porter View Post
It seems that Dolce's big idea has nothing to do with AdS/CFT. He seems to be claiming that quantum mechanics is a manifestation of a compact timelike direction. That is, some time "t" in the future is literally the same as a time "0" in the past; space-time joins up with itself like a donut in which one of the cyclic directions is timelike. Quantum mechanics is to result from imposing these timelike periodic boundary conditions on a classical theory.

But then he talks about individual particles having individual internal times, with the time to repetition depending on the mass. I do not see how to make sense of this. Consider a particle that is created at one point in space, travels through it, and then gets absorbed somewhere else. There's no time loop, so what is the meaning of the "compact internal time" here? The original idea is to take repetitive behavior, like the cycling of the phase factor in an energy eigenstate, and to interpret it the successive cycles as literally identical: the next cycle doesn't just repeat the previous cycle, it is the same thing, because space-time loops back on itself. That might make sense if it was done on a single global scale, like a Godel universe, but how can you apply this interpretation to an object which is clearly created at one time and destroyed at a later time?

Regarding AdS/CFT, he only engages with it superficially. AdS/CFT is an identity of two quantum theories, a correspondence between a quantum string theory in AdS space and a quantum CFT on the boundary of that space. There are lesser versions of the correspondence in which you only concern yourself with a classical limit of the AdS theory, and he seems to be talking about that, and then trying to relate it to his earlier ideas about repeating time. I assure you that there is no proof of AdS/CFT here (and certainly no real discussion of either of the quantum theories in the duality), just some elementary talk about classical boundary conditions in AdS, that are combined in a confusing way with the already confusing ideas about cyclic time.

Quite a few people have tried to get QM from time loops. A few others hope to get quantum mechanics emerging along with gravity and the extra dimension, in an extended version of holographic duality. There are time loops in some versions of AdS. So it would be really interesting if you could indeed get QM on the boundary from time loops in a classical AdS bulk.

But I don't see anything like that here. I suppose it's obvious that I struggle to make sense of the paper, and that I think it is based on conceptual confusions that are hard to track down because they are never explicitly stated and rigorously defined, instead they are spread throughout the text as background assumptions. Maybe I'm missing something and it all makes sense somehow, but really, I doubt it. I have tried at least to pull out some of the component ideas which make sense by themselves, and to indicate how they might have been combined into a comprehensible research program, but I do not think that program is what Dolce is following, he's doing some other confused thing.
You have completely missed the meaning of the idea. Congratulation!

Read "Comments and Outlook" at the end of the first section. Everything is made of particles, particles are clocks (periodic phenomena with cyclic time, as the angular variable in waves), then everything is described by cycles! The (virtual) AdS tells the particle how to vary "ticks" as Schwarzschild metric in gravity. Think a couple of days about that and then let us know.

"The wise man points to the moon, the fool looks at the finger" - Chinese proverb

Quote Quote by mitchell porter View Post
Quite a few people have tried to get QM from time loops. A few others hope to get quantum mechanics emerging along with gravity and the extra dimension, in an extended version of holographic duality. There are time loops in some versions of AdS. So it would be really interesting if you could indeed get QM on the boundary from time loops in a classical AdS bulk.
This is what Dolce does. He derives QM (on the boundary of a virtual extra dimension, which is not a real extra dimension) from time loops of elementary clocks/particles.
mitchell porter
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#9
Feb2-13, 09:34 AM
P: 747
Let's start with something really simple and tell me if you agree with my assessment.

It is possible to build up perturbative quantum field theory from the concept of particles in energy-momentum eigenstates. Interactions can be expressed in terms of annihilation and creation of particles in such states, and then we can construct wavepackets as desired, by summing appropriately over the momentum eigenstates.

Dolce has constructed some sort of correspondence between these space-time-filling, single-particle, energy-momentum eigenfunctions, and classical fields in a space-time with compact periodic time. Many times in his paper, he will mention 4-momentum, and then follow it with a supposedly equivalent statement about 4-periodicity. The question is whether this adds anything of substance to the original theory. So far it seems to be quite superfluous.

Yes, you can take perturbative quantum field theory, and where you would normally talk about 4-momentum eigenstates, you can instead talk about "4-periodicity in the virtual extra dimension". I can only see two ways for this to mean anything: it's a step towards the true physical ontology, or it is a fruitful new mathematical trick. But I don't see how to interpret the locally varying VXD as something real (though presumably Dolce is interested in this option, given his "boson determinism" paper), and I don't see what it allows us to calculate better (I didn't yet try to figure out what's going on in the QGP section, but the derived formulas look relatively elementary).
naturale
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#10
Feb2-13, 09:49 AM
P: 104
You have passed from
Quote Quote by mitchell porter View Post
I do not see how to make sense of this.
to the opposite

Quote Quote by mitchell porter View Post
The question is whether this adds anything of substance to the original theory. So far it seems to be quite superfluous.
The correct attitude is right in the middle between this doesn't "make sense" and this doesn't "add something new". It is like a Copernican revolution, like using the sun as origin of your coordinates rather than the earth, an idea that suddenly simplifies everything. Or like passing from a model with flat earth to a spheric earth. It may seem absurd or trivial, depending on the point of view, but it works.

Quote Quote by mitchell porter View Post
it is a fruitful new mathematical trick
I agree with this. It is more correct to say: extra dimensional formalism is a mathematical trick to describe quantum physics as proposed by Klein. This is the meaning of "virtual" extra dimension and the interpretation to AdS/CFT proposed by Dolce.
BandwagonNinja
BandwagonNinja is offline
#11
Feb2-13, 11:23 PM
P: 5
Thank you very much for posting this Naturale. This is best papers I've read in a while and agree with you that the ideas in here are quite revolutionary. There was one minor thing I didn't understand though, perhaps you can help clear it up. On page 9 Dolce says the periodicity transforms contravariant near eq (9) but near eq (11) he says it transforms as a covariant tangent vector. This is mystify to me.

Mitchell Porter, I quite certain you do not understand what is AdS/CFT. On the other AdS/CFT thread (I can't quote because is locked) you wrote: "AdS/CFT duality is a highly nontrivial equivalence between two quantum theories. The bulk of this paper talks about purely classical relations like boundary conditions. Quantum mechanics hardly shows up, except for a few token comments."

This is just... wrong. Consider Witten quote that appears in Dolce paper. "In AdS/CFT quantum phenomenon are encoded in classical geometry." AdS/CFT correspondence is that the symmetry group of AdS space and 4D conformal theories are the same. It doesn't matter what you do in the AdS space or if you use a classical or quantum field on boundary. The thing that is interesting is that can use string theory and can use QFT.

Quote Quote by mitchell porter View Post
It seems that Dolce's big idea has nothing to do with AdS/CFT. He seems to be claiming that quantum mechanics is a manifestation of a compact timelike direction. That is, some time "t" in the future is literally the same as a time "0" in the past; space-time joins up with itself like a donut in which one of the cyclic directions is timelike.
No that is not Dolce's idea at all. That is Tooker's big idea. You confusing the threads. Dolce only mentions in passing that intrinsic periodicity can be applied to entire universe. Dolce's big idea is to to derive a time from the de Broglie relations and use as a backbone to support a field theory.

Quote Quote by mitchell porter View Post
Consider a particle that is created at one point in space, travels through it, and then gets absorbed somewhere else. There's no time loop, so what is the meaning of the "compact internal time" here?
If read the paper you would see that the internal time is much shorter than the time that is taken between creation and annihilation. Furthermore, you are confusing what Dolce says about isolated systems with more complicated scenarios. Dolce writes:

"However, such a non-elementary system in general has no periodic dynamics, as the ratio of periodicities doe snot necessarily form a rational number."

Quote Quote by mitchell porter View Post
I assure you that there is no proof of AdS/CFT here (and certainly no real discussion of either of the quantum theories in the duality), just some elementary talk about classical boundary conditions in AdS, that are combined in a confusing way with the already confusing ideas about cyclic time.
Again you are confusing this thread with [the other one that has Tooker's paper](http://www.physicsforums.com/showthread.php?t=665116). Dolce makes use of fundamental period of oscillation derived from the de Broglie relations and doesn't use cyclic time for anything but in a brief aside on the few pages Naturale suggested that you read. (I admit I have only read 20 pages, but I do not see cyclic time when I flip forward and it is not relevant to basis of the Dolce inquiry.)
mitchell porter
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#12
Feb3-13, 04:44 AM
P: 747
In order to get on with my life, I would like to withdraw from this discussion. I never wanted to engage with these papers; my first impressions were wholly negative; I only attempted a quick intuitive assessment in order for there to be a counterbalance to naturale's bombast. It would have been wiser to say nothing and to quit is the wise course now.

But I will repeat that AdS/CFT is an equivalence between two quantum theories. The prototypical example is N=4 super-Yang-Mills and the thesis is that it is equivalent to Type IIB string theory in AdS_5 x S^5. These are both quantum theories. That some of the features of the quantum theory on the boundary can be related to classical properties of the bulk, does not mean that the correspondence stops there.
naturale
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#13
Feb3-13, 04:47 AM
P: 104
Quote Quote by BandwagonNinja View Post
Thank you very much for posting this Naturale. This is best papers I've read in a while and agree with you that the ideas in here are quite revolutionary.
Thank you BandwagonNinja

Indeed it is a revolution! - this explains why my other posts on the topic in other threads are mysteriously disappeared, though the idea is published in several peer-reviewed papers and PF rules say "Generally, discussion topics should be traceable to standard textbooks or to peer-reviewed scientific literature."


Quote Quote by BandwagonNinja View Post
There was one minor thing I didn't understand though, perhaps you can help clear it up. On page 9 Dolce says the periodicity transforms contravariant near eq (9) but near eq (11) he says it transforms as a covariant tangent vector. This is mystify to me.
It is a typo. Check the other papers, he always says contracovariant tangent vector.
naturale
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#14
Feb3-13, 05:10 AM
P: 104
Quote Quote by mitchell porter View Post
In order to get on with my life, I would like to withdraw from this discussion. I never wanted to engage with these papers; my first impressions were wholly negative; I only attempted a quick intuitive assessment in order for there to be a counterbalance to naturale's bombast. It would have been wiser to say nothing and to quit is the wise course now.

But I will repeat that AdS/CFT is an equivalence between two quantum theories. The prototypical example is N=4 super-Yang-Mills and the thesis is that it is equivalent to Type IIB string theory in AdS_5 x S^5. These are both quantum theories. That some of the features of the quantum theory on the boundary can be related to classical properties of the bulk, does not mean that the correspondence stops there.
You are welcome in this discussion. Criticisms are vital in science. But sometimes, papers are so original that it is not sufficient a rapid scan to understand them. It is necessary to follow the derivation of the idea and see if it really works, step after step. Try and you'll see. Science is this! This is the scientific method!


This idea cannot be ignored.


AdS/CFT, like string theory, after many years of speculations, allows several different interpretations ("one for every taste"). This paper tries to restart from ground zero, to reconsider the foundations of both. They are amazing mathematical properties (ex: classical to quantum correspondences). There is surely something correct. Dolce has tried to find the correct idea at the base of the complicated universe of AdS/CFT, avoiding crap things. He is not a criminal.

You may think this is in competition with mainstream researches. On the contrary, it is a new possibility for physics. If you are a researcher you probably dream to be part of a Copernican revolution, this idea looks like chance.
LBloom
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#15
Feb3-13, 03:54 PM
P: 173
This is just... wrong. Consider Witten quote that appears in Dolce paper. "In AdS/CFT quantum phenomenon are encoded in classical geometry." AdS/CFT correspondence is that the symmetry group of AdS space and 4D conformal theories are the same. It doesn't matter what you do in the AdS space or if you use a classical or quantum field on boundary. The thing that is interesting is that can use string theory and can use QFT.
No actually mitchellporter is right. The AdS/CFT correspondence is not just that the symmetry group of AdS space and 4D conformal theories are the same. The fact they are the same points towards a duality, but this coincidence does not a duality make. In order to proof there is actually a duality between two theories you have to do nontrivial checks, like calculating the partition function and some correlation functions. The most famous example that mitchellporter brings up has been heavily tested (and is between two quantum theories) and there are plenty of similar dualities we don't fully understand, even though we know the symmetry groups match.

Also even though the duality relates quantum aspects of one theory to classical aspects of another doesn't imply any quantum/classical correspondence. In the weakly coupled limit of string theory we obtain objects from classical geometry (as we should if it and SUGRA are to reduce to GR), but the duality from which these relations spring is still between quantum theories and hopefully still holds for all values of the coupling constant.

Quote by mitchell porter

Are you the author?

No. I'm not the author.
http://physicsforums.com/showthread.php?t=664870
http://physicsforums.com/showthread.php?t=307961
http://physicsforums.com/showthread.php?t=424860
http://physicsforums.com/showthread.php?t=310733&page=2

If you're not the author you sure do show an affinity for his work.
BandwagonNinja
BandwagonNinja is offline
#16
Feb3-13, 04:07 PM
P: 5
It is my understanding that AdS/CFT is fundamental a correspondence between abstract mathematical objects. The theories we can build in these objects are very interest, and that why there is interest in AdS/CFT. AdS/CFT is the narcissus name for holography principle no? Perhaps I am mistaken, but you have not convinced me. Perhaps you and I make semantics.
LBloom
LBloom is offline
#17
Feb3-13, 05:22 PM
P: 173
It is my understanding that AdS/CFT is fundamental a correspondence between abstract mathematical objects. The theories we can build in these objects are very interest, and that why there is interest in AdS/CFT. AdS/CFT is the narcissus name for holography principle no? Perhaps I am mistaken, but you have not convinced me. Perhaps you and I make semantics.
AdS/CFT dualities obey the holographic principle, but not vice versa. That is the holographic principle is an older and broader concept then AdS/CFT. AdS/CFT refers specifically to just one kind of duality where the holographic principle comes into play.

The AdS/CFT duality is not a correspondence between abstract mathematical objects, it is a relation between a CFT in d-1 dimensions to string theory (or a theory whose origin is in ST) in d dimensions. Neither of these are well defined mathematical objects. There are QFTs that have been put on a rigorous footing by mathematicians, but for the most part this is not the case.

To a certain extent there is some bad language at play. AdS/CFT has become a catchall for many different ideas and for holography in general, although it is just one subset of ideas.
naturale
naturale is offline
#18
Feb4-13, 04:51 AM
P: 104
Quote Quote by LBloom View Post
No actually mitchellporter is right. The AdS/CFT correspondence is not just that the symmetry group of AdS space and 4D conformal theories are the same. The fact they are the same points towards a duality, but this coincidence does not a duality make. In order to proof there is actually a duality between two theories you have to do nontrivial checks, like calculating the partition function and some correlation functions. The most famous example that mitchellporter brings up has been heavily tested (and is between two quantum theories) and there are plenty of similar dualities we don't fully understand, even though we know the symmetry groups match.
Please look at eq. 2.11 of Witten paper hep-th/9892150. He then writes: "The generating function of these correlation functions [quantum] would be the partition function [classical] of the conformal field theory ..." Then you can quantize as much as you want things that are already quantized, but you wont describe reality. The central meaning of AdS/CFT is give by eq. 2.11 (or similar).


Dolce has derived that equation just from clocks.


Also even though the duality relates quantum aspects of one theory to classical aspects of another doesn't imply any quantum/classical correspondence. In the weakly coupled bla bal bla... .
If, as you say, "duality relates quantum aspects of one theory to classical aspects of another", where is the quantization? Where does QM emerge? Dolce answers to this simple question, He concludes that quantization is in the (virtual) extra dimensional formalism.



If you're not the author you sure do show an affinity for his work.
His arguments are correct, if you believe in mathematics.


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