Holographic Dualities and the Potential Misdirection of String Theory

  • Thread starter inflector
  • Start date
341
2
In another thread: https://www.physicsforums.com/showthread.php?t=436080" a discussion came up relating to the validity of String Theory and the specific thought that, if nothing else, it has helped us to better understand the issues of quantum gravity. I wanted to start a new thread to adress this specific point so as not to take the other thread off topic.

Some background. First we have atyy:
Also, it is known that our best theories which do work break down at a high enough energy, and some theory must replace them. So by mathematical consistency alone, we have to search for a new theory. At present, string theory is without doubt an approach that has taught us a lot about whatever the true theory of quantum gravity is, even if it ultimately turns out that string theory does not model nature.
Then bcrowell replied:
I'm not convinced that this is true. It may have taught us absolutely nothing about the true theory of quantum gravity. It may have hindered us from finding a true theory of quantum gravity, in the same way that Aristotelian physics hindered Galilean physics from being created.
I'd take this a bit further. It is possible that the progress of string theory has hindered us by pointing us in the exact opposite direction from where we'd need to go to solve quantum gravity.

To illustrate what I mean, I need the next reply of atty:
Do you think these statements are false?

http://arxiv.org/abs/0809.4266
"These dualities become especially powerful when combined with string theory [1]. It is an occasional misconception, however, that the existence of holographic dualities is contingent on the validity of string theory. This is not the case."

Or that this approach is misguided?

http://arxiv.org/abs/1006.1902
"Ever since the seminal work of Bekenstein and Hawking, it has been clear that there is a deep and fundamental relation between gravity, thermodynamics and quantum mechanics, while its detailed form and origin was and is largely mysterious. ... It seems likely that the basic triangular relationships transcend string theory and AdS/CFT, although lessons from string theory are likely useful guides for unraveling the more general picture. It is our hope that the attempt here to generalize fluid/gravity duality away from the stringy context to its most essential ingredients may be useful in understanding this triangle."

(emphasis mine)
Both of these papers cover issues related to holographic dualities and their role in quantum gravity.

The general idea of a holographic duality for quantum gravity is that there is a correspondence between a theory with gravity in a particular dimension and a quantum field theory of one less dimension without gravity. The most famous example being the AdS/CFT correspondence originally proposed by Juan Maldacena. The AdS/CFT correspondence specifically relates to the correspondence of a string theory with gravity to a quantum field theory without gravity.

In http://homepage.mac.com/photomorphose/documents/qpdf.pdf" [Broken]:
More precisely, the theories predict that the number of dimensions in reality could be a matter of perspective: physicists could choose to describe reality as obeying one set of laws (including gravity) in three dimensions or, equivalently, as obeying a different set of laws that operates in two dimensions (in the absence of gravity). Despite the radically different descriptions, both theories would describe everything that we see and all the data we could gather about how the universe works. We would have no way to determine which theory was “really” true.

Such a scenario strains the imagination. Yet an analogous phenomenon occurs in everyday life. A hologram is a two-dimensional object, but when viewed under the correct lighting conditions it produces a fully three-dimensional image. All the information describing the three-dimensional image is in essence encoded in the two-dimensional hologram. Similarly, according to the new physics theories, the entire universe could be a kind of a hologram.
It is an interesting and mathematically clever idea and one that ties into String Theory, though it is not exclusive to it. The implication of this holographic duality and way of thinking that I wish to address here is that it implies that gravity and even the perception of the extra dimension are emergent. The duality allows one to work in a lower-dimension quantum field theory and then the extra dimension and gravity emerge in the higher dimension through the duality.

The mathematics involved is by Maldacena's own admission difficult as thus far the conjecture itself has not been proved:
Since [the introduction of the AdS/CFT correspondence conjecture in 1997], many researchers have contributed to exploring the conjecture and generalizing it to other dimensions and other chromodynamics theories, providing mounting evidence that it is correct. So far, however, no example has been rigorously proved— the mathematics is too difficult.
Now, back to the statement by bcrowell:
[String Theory] may have taught us absolutely nothing about the true theory of quantum gravity. It may have hindered us from finding a true theory of quantum gravity, in the same way that Aristotelian physics hindered Galilean physics from being created.
The idea that gravity emerges from a theory operating at a lower dimension has two specific implications with respect to the complexity of the task of developing a theory of quantum gravity:

1) That one should be searching for potential correspondences which may map onto what we believe represents our actual space-time rather than the easier to work with AdS. This is very complicated.

2) That one should search for the ways in which gravity and dimensions can emerge from the lower-dimensional quantum field theories. This too is complicated because the number of ways in which something can emerge from a complicated theory is itself necessarily complicated. Emergence is not an easy phenomena to derive or explain a priori. Its very essence is that it is an unexpected complex outcome from a set of simpler rules. Emergence is complexity to some power greater than one.

Now it is possible that a holographic duality underlies quantum gravity and that it is indeed emergent. There are lots of physicists betting that way. But this is necessarily a complicated path and one in which it will be difficult to make headway.

It is also possible that it is not emergent but, in fact, is fundamental. Not too many physicists, by comparison, are exploring this option.

If this proves to be true at some future date and gravity ends up being fundamental, then one will then be able to argue that this offshoot of String Theory—the holographic duality which atyy used as his example of a contribution of String Theory—had led physics down the wrong path, and even the opposite path from the one required to reach a theory of quantum gravity.

Time will tell.

It seems to me that it makes sense to explore all options.
 
Last edited by a moderator:

atyy

Science Advisor
13,342
1,490
It is also possible that it is not emergent but, in fact, is fundamental. Not too many physicists, by comparison, are exploring this option.

If this proves to be true at some future date and gravity ends up being fundamental, then one will then be able to argue that this offshoot of String Theory—the holographic duality which atty used as his example of a contribution of String Theory—had led physics down the wrong path, and even the opposite path from the one required to reach a theory of quantum gravity.

Time will tell.

It seems to me that it makes sense to explore all options.
Yes. The other option is called "Asymptotic Safety". Polchinski states both options at the start of his string theory textbook, and says the other one is not ruled out: "There are two possible resolutions. The first is that the divergence disappears ... when the theory is treated exactly. In the language of the renormalization group, this would be a nontrivial UV fixed point. The second is that the extrapolation of the theory to arbitrarily high energies is incorrect." http://books.google.com/books?id=k4ZQ04viGWIC&printsec=frontcover&dq=polchinski+string&source=bl&ots=XIoQ2ryHwh&sig=tJi_QMtTdyi16KTEfNVEgBLSAEE&hl=en&ei=7u2wTNPUNIL6lweLvfXmDw&sa=X&oi=book_result&ct=result&resnum=4&ved=0CBsQ6AEwAzgK#v=onepage&q&f=false

Weinberg has advocated the study of both "Asymptotic Safety" and string theory.

Polchinski is a major contributor to the understanding of renormalization, and his equation is a key tool in Asymptotic Safety.

http://relativity.livingreviews.org/Articles/lrr-2006-5/ [Broken]
 
Last edited by a moderator:
308
0
Have they reconciled asymptotic safety with black hole entropy? Haven't heard on this in a while but I haven't checked either. If not then asymptotic safety just can't work. How do you match the degrees of freedom?

Also, there's no such thing as a "wrong" or "right" "path" in physics. The results are either correct or not.
 

atyy

Science Advisor
13,342
1,490
Have they reconciled asymptotic safety with black hole entropy? Haven't heard on this in a while but I haven't checked either. If not then asymptotic safety just can't work. How do you match the degrees of freedom?

Also, there's no such thing as a "wrong" or "right" "path" in physics. The results are either correct or not.
And string theory is proven to work?
 
To a certain extent yes, Asymptotic Safety does too.


"1. Gravity. Every consistent String Theory must contain a masless spin-2 [vibrational] state, whose interactions reduce at low energy to general relativity.

2. A consistent theory of quantum gravity, at least in perturbation theory. As we have noted, this is in contrast to all known quantum field theories of gravity.

3. Grand unification. String theories lead to gauge groups large enough to include the Standard Model. Some of the simplest string theories lead to the same gauge groups an fermion representations that arise in the unification of the Standard Model.

4. Extra dimensions. String theory requires a definite number of space-time dimensions, ten [or 11 in M-Theory]. The field equations have solutions with four large flat and six small curved dimensions, with four dimensional physics that resembles the Standard Model.

5. Supersymmetry. Consistent String Theories require space-time supersymmetry, as either a manifest or a spontaneously broken symmetry

6. Chiral gauge couplings. The gauge interactions in nature are parity asymmetric (chiral). This has been a stumbling block for a number of previous unifying ideas: they required parity symmetric gauge couplings. String theory allows chiral gauge couplings.

7. No free parameters. String theory has no adjustable constants.

8. Uniqueness. Not only are there no continuous parameters, but there is no discrete freedom analogous to the choice of gauge group and representations in field theory: there is a unique string theory." - (String Theory, Volume 1: An Introduction to Bosonic String, Polchinski)

The Holographic Principle also provides insight into the nature of space-time and gauge-gravity duality has proven to be an important feature of understanding the structure of space time and Quantum Field Theory.
 
Last edited:

MTd2

Gold Member
2,026
25
As far as I know Asymptotic Safety is not a theory, but a hypothesis of a mathematical property. Like a big elephant in the small room that was ignored and may make several theories that were non renormalizable normalizable.
 

atyy

Science Advisor
13,342
1,490
As far as I know Asymptotic Safety is not a theory, but a hypothesis of a mathematical property. Like a big elephant in the small room that was ignored and may make several theories that were non renormalizable normalizable.
Yes, I see that's how Percacci is using the term. So I should have said Asymptotic Safety of Einstein gravity.
 

tom.stoer

Science Advisor
5,759
157
The holographic principle comes in different forms. Firstly it relates entropy with area instead volume; secondly it relates the surface degrees of freedom with the volume degrees of freedom.

I now that some people don't like it, but we have to mention LQG from which an two-dim. "horizon" theory emerges when applied to black holes. So it seems that neither the first nor the second step are specific to string theory.

For me this means that all theories incorporating the holographic principle in some way or the other are candidates for a theory of quantum gravity.
 

Fra

3,055
135
I personally still consider the "holographic principle" to be far from even understood and properly formulated, and wether it's somehow universally fixed or somehow emergent as an equilibrium condition.

But it's clear that all the hints, and similarities suggest that there IS something interesting here. But we don't yet understand it, and as I see it the main hints doesn't come from ST.

So this general quest has IMO nothing at all specific to do with ST. So I agree with Tom.

Probably what we need to do, is to understand the functional meaning of information(and entropy) and what the connection between entropy and action is, and what this means in a picture of interacting quantum observers. I don't see how ST framework is anywhere near giving an acceptable handle on these questions.

/Fredrik
 
341
2
Have they reconciled asymptotic safety with black hole entropy? Haven't heard on this in a while but I haven't checked either. If not then asymptotic safety just can't work. How do you match the degrees of freedom?.
This idea seems wrong for two reasons:

1) The lack of a reconciliation today does not mean that someone won't come up with one in the near future. There are scientists working on every single one of the major holes in any major potential new theory for gravity.

2) The very idea of the need for any theory of quantum gravity to reconcile specifically with black hole entropy seems to me to be completely flawed in an almost self-parodic circular manner. I mean, isn't one of the reasons that we are looking for a new theory because we specifically don't know what happens at the singularities like the big bang and black holes since GR and quantum mechanics conflict there? So why would we require a theory that is supposed to contain the equations defining the behavior of a black hole to conform to predictions of models that were built before we had a valid theory and equations defining behavior of a black hole? Don't we know we can't trust our predictions in a regime where at least one of the two most tested theories we have must be wrong, or both? The math won't have it any other way. Not only that, we don't even know that black holes exist as we currently conceive them. The requirement that a theory of quantum gravity needs to reconcile itself with our current broken theory doesn't make any sense to me at all.

What am I missing?
 
308
0
It's called consistency check. Whatever new revolutionary theory you find that we never thought about still has to be perfectly consistent with what we already know.

It doesn't even matter if black holes exist or not.
 

MTd2

Gold Member
2,026
25
AS is not a theory. Just like renormalizaton and regularization aren't. Those are just methods. But AS needs more work.
 

tom.stoer

Science Advisor
5,759
157
The very idea of the need for any theory of quantum gravity to reconcile specifically with black hole entropy seems to me to be completely flawed in an almost self-parodic circular manner. I mean, isn't one of the reasons that we are looking for a new theory because we specifically don't know what happens at the singularities like the big bang and black holes since GR and quantum mechanics conflict there?

...

What am I missing?
I think you are missing the fact that both string theory and loop quantum gravity are theories of quantum gravity which are mathematically well defined and which allow in certain regimes (approximations) to calculate what happens inside a black hole.

In string theory the microstates of a black hole can be calculated for extremal black holes (BPS state) exactly. In LQG there is the symmetry-reduced LQC theory which shows that the singularity is resolved. In addition full LQG provides a means to understand the microstates as well.
 
Last edited:
341
2
It's called consistency check. Whatever new revolutionary theory you find that we never thought about still has to be perfectly consistent with what we already know.

It doesn't even matter if black holes exist or not.
If it doesn't matter if black holes exist then how can you say that if asymptotic safety cannot be reconciled with black hole entropy then it can't work. How does the particular traits of a potentially non-existent entity constrain quantum gravity theory?

Yes, any new theory still has to be consistent with what we already know.

But we don't know anything about black holes.

Nothing at all. We don't even know they exist. We think they exist. We have seen lots of evidence that there is something really massive that isn't a star at the center of our galaxy and of others we have studied. We have seen signs that fit theories we have about how black holes work assuming GR holds.

But we do know that GR doesn't hold at extreme energies confined to extremely tiny space as is predicted for a black hole. We need a quantum gravity theory to tell us about that regime. That's why so much effort is going into discovering one. So we don't know anything about that regime. We have a theory that we know doesn't work there, so we know our theorizing about what happens there is likely to contain at least some error.

The new theory might not have the same prediction for black hole entropy. The new theory might even show that black holes as we think of them right now cannot exist and it may provide an even better explanation for what is happening at the center of our galaxies than the current supermassive black hole hypothesis.
 
341
2
I think you are missing the fact that both string theory and loop quantum gravity are theories of quantum gravity which are mathematically well defined and which allow in certain regimes (approximations) to calculate what happens inside a black hole.
No, I'm not missing this fact. I just don't find it at all relevant. String theory needs to be consistent with itself. Loop quantum gravity needs to be consistent with itself.

Another different theory of gravity does not need to be consistent with string theory or loop quantum gravity because it is a different theory, this different theory of gravity only needs to be mathematically consistent with itself and known experimental observation. What string theory calculates to be the behavior of black holes does not matter if string theory is not correct.

In string theory the microstates of a black hole can be calculated for extremal black holes (BPS state) exactly. In LQG there is the symmetry-reduced LQC theory which shows that the singularity is resolved. In addition full LQG provides a means to understand the microstates as well.
That's wonderful for string theory and LQG, but again, irrelevant for another theory that does not rely or or extend either one of those theories.

Why do you think that string theory's description of black hole properties is relevant to another theory that is not derivative of string theory?

You may assume that string theory is correct but that doesn't mean that someone who is working on another theory is going to make the same assumption. In fact, they'd be foolish to develop a theory that they didn't think was even possibly correct.
 

tom.stoer

Science Advisor
5,759
157
It's like in the early days of quantum mechanics: the Bohr-Sommerfeld model of atom was - strictly speaking - wrong. Nevertheless it told us some truth about atoms, energy levels etc. Sometimes theories make reasonable predictions beyond their regime of applicability.

Another thing: LQG and ST have nearly NOTHING in common. Nevertheless in some regimes they arrive at nearly identical predictions. For BH entropy the predictions fit to the Bekenstein-Hawking result which has nearly nothing in common with both LQG and ST. I would say that these fascinating results are good indications that LQG and ST are good approximations of some underlying truth of nature.
 
341
2
It's like in the early days of quantum mechanics: the Bohr-Sommerfeld model of atom was - strictly speaking - wrong. Nevertheless it told us some truth about atoms, energy levels etc. Sometimes theories make reasonable predictions beyond their regime of applicability.
Yes, they do. Physicists, astronomers, and mathematicians are generally very smart people so even if their ideas are in error it is likely that they are not completely without merit. For this reason, successful new theories don't generally completely replace old ones, they usually extend them into new domains and clarify them.

Another thing: LQG and ST have nearly NOTHING in common. Nevertheless in some regimes they arrive at nearly identical predictions.
This might be due to the fact that LQG and ST theorists have been trying to match the prior predictions because, all else being equal, that makes the theory easier to accept. It also makes it less falsifiable.

For BH entropy the predictions fit to the Bekenstein-Hawking result which has nearly nothing in common with both LQG and ST. I would say that these fascinating results are good indications that LQG and ST are good approximations of some underlying truth of nature.
Sure, they might be. But they might also be simply evidence that physicists can be mighty clever when they need to be. Holographic dualities are one great example. The idea was specifically developed to match the results of Bekenstein and Hawking. Should we be surprised that it solves the problem for which it was created?

Perhaps it is indicative of some underlying truth of nature. I think most physicists would bet that way. But it might just be indicative of the cleverness of 't Hoof, Susskind, Maldacena, et al.

So until we have a theory of quantum gravity that we understand and have tested we can't be sure that this is the case.
 

tom.stoer

Science Advisor
5,759
157
This might be due to the fact that LQG and ST theorists have been trying to match the prior predictions because, all else being equal, that makes the theory easier to accept. It also makes it less falsifiable.
I don't think it's up to you to question the integrity of research groups!

Especially for LQG and ST contrasting results would have been welcome in both "factions" over the years as it would allow for a clearer assessment regarding the validity of both theories.

Holographic dualities are one great example. The idea was specifically developed to match the results of Bekenstein and Hawking. Should we be surprised that it solves the problem for which it was created?
The idea of ART was developed to solve the problem of perihelion precession - and it worked. What do you want to insinuate?

... it might just be indicative of the cleverness of 't Hoof, Susskind, Maldacena, et al.
You can be sure about that!

So until we have a theory of quantum gravity that we understand and have tested we can't be sure that this is the case.
As I just wanted to point out we have mathematically consistent theories of quantum gravity - and we understand them to some extend. About testability you are right, that's a major problem. But you can't blame the theoretists for the smallness of the Planck length.

What we are facing is a paradigm shift how to do physics (I am not talking about landscapes here). There is a shift from experimental guidance towards mathematical principles.
 
308
0
I still don't understand why so many are surprised that string theory (or QG in general) is failing to produce experimental predictions. You think the Planck length was discovered to be so small in the last few years? No, this was known since people first started thinking about the issue many decades ago. It's not news to anyone what the situation is.

If black holes don't exist, you're going to need a reason for why they shouldn't exist. They're a solution of GR, so unless GR is wrong even in its usual regime, any QG theory will need to reproduce them, including their entropy.
 

Fra

3,055
135
I partly symphatise with the general scepsis that new hypothesis should be tested against somewhat verified experiments and not necessarily against pure expectations based on competing hypothesis that may or many not hold true.

As an example, I for example personally think that at some point we we may need to rework the basic structure of QM. QM is extremely well tested, but as we also konw, only for specific domains! In particular those where we are studying small subsystems in a highly controlled much more massive context (ie. particle/atomic physics) Some people think that this success means it's extrapolation to arbitrary cases and scales must be true as well. This isn't so. Even if it turns out to be, it's far from obvious. In particular is it not obvious that the abstration making sense for studying a subsystem makes sense in a cosmological perspective.

So if we a new theory does not reproduct the exactr structure of QM or GR in all domains, but only in the respective domains where they are experimentally verified that's fine as well. It's just that I think alot of people find it hard to imagine how a new theory can comply to QM predictions to the extreme accuract it's known to hold, and still violated it's general principles in other domains.

But to get back to holography, it seems inflector thinks something is wrong about the holographic principle; then I would guess the maybe you have some own idea of why or how? Maybe it's easier to accept your arguments if there is a good alternative? Somehow if there is not other options, using the "extrapolations or expectation" from semiclassical theory seems like the only rational guide. In my example above, I wouldn't personally think QM needed to change if I didn't have the slightest clue how. It's somehow not rational to throw away the only clues you have, until you have something that appears more promising.

Maybe it would be interesting to just discuss some alterantives to the holographic principles? or maybe equivalently, alternative meanings of it? Inflector?

/Fredrik
 

Want to reply to this thread?

"Holographic Dualities and the Potential Misdirection of String Theory" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top