AdS/CFT as quantum to classical correspondenceby naturale Tags: ads/cft, kaluzaklein, quantization 

#1
Jan3113, 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 extradimensional theories. Its ansatz is that every particle is a reference clock. It is a peerreviewed 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 spacetime dimensions the assumption of periodic boundary conditions represents a consistent semiclassical 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 fourdimensional theory is manifestly dual to an extradimensional field theory. The resulting correspondence between extradimensional geometrodynamics and ordinary quantum behavior can be interpreted in terms of AdS/CFT correspondence. By applying this approach to a simple QuarkGluonPlasma freezeout model we obtain fundamental analogies with basic aspects of AdS/QCD phenomenology. Subjects: High Energy Physics  Theory (hepth); High Energy Physics  Phenomenology (hepph) Journal reference: Annals of Physics, Volume 327, Issue 9, September 2012, pp 23542387 http://arxiv.org/abs/1110.0316 



#2
Feb113, 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.




#3
Feb213, 05:55 AM

P: 748

Are you the author?




#4
Feb213, 06:17 AM

P: 104

AdS/CFT as quantum to classical correspondence"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 



#5
Feb213, 06:18 AM

P: 748

Why do you have such confidence in the correctness of his work?




#6
Feb213, 06:23 AM

P: 104





#7
Feb213, 07:08 AM

P: 748

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; spacetime 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 spacetime 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. 



#8
Feb213, 08:03 AM

P: 104

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 



#9
Feb213, 09:34 AM

P: 748

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 energymomentum 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 spacetimefilling, singleparticle, energymomentum eigenfunctions, and classical fields in a spacetime with compact periodic time. Many times in his paper, he will mention 4momentum, and then follow it with a supposedly equivalent statement about 4periodicity. 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 4momentum eigenstates, you can instead talk about "4periodicity 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). 



#10
Feb213, 09:49 AM

P: 104

You have passed from




#11
Feb213, 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. "However, such a nonelementary system in general has no periodic dynamics, as the ratio of periodicities doe snot necessarily form a rational number." 



#12
Feb313, 04:44 AM

P: 748

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 superYangMills 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. 



#13
Feb313, 04:47 AM

P: 104

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 peerreviewed papers and PF rules say "Generally, discussion topics should be traceable to standard textbooks or to peerreviewed scientific literature." 



#14
Feb313, 05:10 AM

P: 104

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. 



#15
Feb313, 03:54 PM

P: 173

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. 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. 



#16
Feb313, 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.




#17
Feb313, 05:22 PM

P: 173

The AdS/CFT duality is not a correspondence between abstract mathematical objects, it is a relation between a CFT in d1 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. 



#18
Feb413, 04:51 AM

P: 104

Dolce has derived that equation just from clocks. 


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