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inflector

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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:

Then bcrowell replied:

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:

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" :

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:

Now, back to the statement by bcrowell:

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.

Some background. First we have atyy:

atyy said: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:

bcrowell said: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:

atyy said: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 beenclear 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 thebasic 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" :

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:

bcrowell said:[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.

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