# Holographic Dualities and the Potential Misdirection of String Theory

MTd2
Gold Member
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.
This is another point that will probably be raised in the next years. If no particles that are significantly responsible for Dark Matter are found, the validity of GR will be questioned too. That's quite a limbo for fundamental science.

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 a new theory does not reproduct the exact 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.
(emphasis mine)

This last paragraph gets to the point I am trying to make. In particular the sentence I bolded.

I also strongly agree with the last sentence. A lot of people do find it hard to imagine this.

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?
No, actually I don't have a strong opinion of the holographic principle. It is an idea that is clever that has some intuitive validity. It solves a problem.

I was using it as an example of something that COULD BE WRONG, and therefore that COULD BE LEADING US DOWN THE WRONG PATH. I am NOT PROPOSING specifically that I have some reason to believe THAT IT ACTUALLY IS WRONG. I don't know.

The difference between my thinking and many others here (or at least my read on their thinking) is that I tend to look at most ideas tentatively, even ones that are well accepted, because I believe that there is some set of assumptions, or perhaps only one, that science currently holds which is in error. And that this error in assumption is keeping us from seeing the key to the solution to quantum gravity. I believe it is probable that at least one cherished idea is wrong or only partially correct and that we can't see the solution because our assumptions cloud our perception of what is possible.

That is why I have been trying to differentiate very intentionally between what we actually know through experiment and direct observation and the interpretation of those experiments and observations that we currently hold.

I also believe that it is likely that the theory of quantum gravity that science ends up accepting will be able to be experimentally and observationally confirmed.

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.
This is not an unreasonable initial approach. However, after as many years as we have been searching for a theory of quantum gravity, it makes sense to consider alternatives where our extrapolations might not hold.

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.
I find that it is often helpful after one has carefully considered a given assumption for a long time to imagine what it would be like if the assumption were not true or even if the opposite were true. If you can imagine scenarios which are just as likely in the event your assumption does not hold or that its opposite holds, this is an indication that the assumption should not be assumed but held open as only a possibility.

Maybe it would be interesting to just discuss some alternatives to the holographic principles? or maybe equivalently, alternative meanings of it? Inflector
Consider the goal for which the holographic principle was developed: to match the entropy of black holes which is theorized to scale as $$r^2$$ rather than as $$r^3$$ as one might expect.

Here are the relevant points with respect to the holographic principle as it stands:

• There is a correspondence between a lower dimensional theory without gravity and a higher dimension
• Gravity is emergent in this higher dimension
Another possibility is that the idea of a holographic projection holds but from the exact opposite perspective:

• Gravity is fundamental in a higher dimension where black hole entropy scales as $$r^3$$ say for example because a black hole is a 3D object in 4D space
• In one lower dimension entropy scales as $$r^2$$
Another possibility is that:

• The idea of a holographic projection between dimensions doesn't hold
• Entropy scales as $$r^2$$ for another theoretical reason
Finally, it could be true that:
• Our theory of black holes is not correct, they don't exist as we currently conceive them
• Entropy for the black hole replacement in the new theory scales as $$r^3$$

I believe that any one of these possibilities could be true.

For this reason, I don't believe that one should assume that gravity is emergent when trying to build a theory of quantum gravity. That is one possibility. The other alternative, that it is fundamental, should also be considered and developed too.

So it's natural that they focus on similar problems, but that does not mean that they "try to match" and "fiddle their calculations" in order to make them easier to accept.
I should have chosen different words.

I didn't mean that they were trying to fiddle with their results, and I didn't intend the wording of "easier to accept" to imply that they were doing anything nefarious or for marketing purposes only.

I think it is quite natural when developing a new theory that one tries to derive existing theoretical expectations. That is the whole reason that the correspondence principle is important. A theory that can show that it reproduces the results of existing theory in well tested domains will be more easily accepted. That's all I meant. I think this is a good thing, not a bad one.

No, that's unfortunately no longer true. In the QG regime we are hardly able to test theories against experiments (even so this is desired). That means the "can't do ..." does no longer work.
It may be that they can't be tested, that's different than what I was trying to point out. I said: "match the data that you know already exists." If a theory covers a domain that can't be tested, say the Planck scale, then there is no data for that domain.

I meant matching experimental results that we already have, not new experiments that we can't run because of limits to our current technology. So, for example, if you have a theory that can't explain the Bell's Inequalities test results, that theory doesn't work and must be discarded or fixed.

tom.stoer
The difference between my thinking and many others here ... is that I tend to look at most ideas tentatively ... because I believe that there is some set of assumptions ... that science currently holds which is in error. And that this error in assumption is keeping us from seeing the key to the solution to quantum gravity.
I don't think so. Up to now there is reason to believe that any fundamental principle is wrong. It's just that QG is currently neither verifiable nor falsifiable in the QG domain.

As long as there are no hints that something goes wrong experimentally, I can't see any reason why we shouldn't use these well-established principles. Changing some basic principle doesn't make QG falsifiable / experimentally testable!

But changing some principle may spoil correct predictions of the QG theories in the experimentally testable domain (were we do not need them, but only check their consistency); we do not want this to happen.

They way I personally elaborate these holographic connections has nothing directly to do with black holes ONLY. One can consider arbitrary boundaries and subsets and generic observer horizons. So IMO, there are (in the future) possible implications of this that may be tested in different ways, not necessarily ONLY for BH horizons. At least that's how I think of it.
This makes good sense. If the holographic principle holds then we should see other evidence of it and other ways it affects our 4D world. In fact, it should be possible to find areas where one could make a prediction which could be confirmed by experiment, one would think.

tom.stoer
Nice turn!

This is indeed how many people today think about holography. The volume degrees of freedom of a certain system are represented by a boundary Hilbert space living on the surface. These boundaries need not be physical; they can be introduced rather artificially, e.g. as boundary between a "quantum system" and an "observer". Then the Hilbert space structure encodes naturally what we (= the observer) can know about the system, as we (the observer) have defined what this system really _is_ - namely in drawing the boundary.

I don't think so. Up to now there is reason to believe that any fundamental principle is wrong. It's just that QG is currently neither verifiable nor falsifiable in the QG domain.

As long as there are no hints that something goes wrong experimentally, I can't see any reason why we shouldn't use these well-established principles.
I understand your position, and most scientists probably hold the same view that you do.

I see hints all over the place that "something is wrong experimentally.":

• Galaxy rotation curves and the need for dark matter which we can't yet detect
• The large-scale structure of the universe
• The pioneer anomaly
• The flyby anomaly
• Dark energy
• Ultra high energy cosmic rays (OMG particles)
• The recent detection of changes in radioactive emission tied to the sun and solar flares

These unexplained phenomena tell me that some part of current theory is wrong or incomplete.

Changing some basic principle doesn't make QG falsifiable / experimentally testable!
Not by itself it doesn't you are right. Just changing widely-held assumptions doesn't guarantee success or a testable theory. Nevertheless, a theory that changes one of our unproven but still widely held assumptions might have features that are unexpected but testable.

All of the above list of "hints" could potentially be explained by some sort of bizarre gravity scenario and this idea would be testable. For example, consider the pioneer anomaly, if we have observed effects using probes we have sent already using early 1970s technology, it stands to reason that we'd see the same effects if we sent new probes specifically to test a given theory if the new bizarre theory is valid.

Suppose this new theory of gravity predicts anisotropies in gravitational mass and that gravity is a statistical phenomena on the large scale but anisotropic on the level of an individual particle. Suppose, again that it is posited that this new theory can explain the pioneer anomaly, ultra-high-energy-cosmic rays, and the existence of dark matter. The ability to tie the predictions of this new theory to specific observational anomalies also would imply the ability to test it further through observation and experiment. Anisotropy in gravity is something we could test using current technology if that is what is behind the acceleration anomalies I listed above.

This is just one very hypothetical example of how discarding a widely held assumption, in this case gravitational isotropy, could lead to a testable theory.

This is admittedly, not the path most would take. Nevertheless, I do think it represents one approach that should be developed.

Fra
> Nice turn!

I agree :) now we're closing in.

> In fact, it should be possible to find areas where one could make a prediction which could be confirmed by experiment, one would think.

This is my conviction as well, but before we get there, the exact formulation and meaning is still unclear.

For example

> Then the Hilbert space structure encodes naturally what we (= the observer) can know about the system

One may ask, what DIFFERENCE does it make, what the observer knows? ;-) Unless we just thinkg of knowledg or "information" in a realist sense, we need to have some ideas to make sense of this.

The idea I have is the idea of rational action, which means that this has implications for how the observer ACTS onto it's environment. This can (with some work) possibly give plenty of predictions, that does not need black holes produced in labs.

/Fredirk

If black hole entropy is not proportional to area, then QFT is wrong as well. You can do the computation when the curvature is not very big, and that's what you get. Higher order corrections are not going to change area to volume.

You are expecting way too many things to be wrong just in order to accommodate nothing in return.

If black hole entropy is not proportional to area, then QFT is wrong as well. You can do the computation when the curvature is not very big, and that's what you get. Higher order corrections are not going to change area to volume.

You are expecting way too many things to be wrong just in order to accommodate nothing in return.
Who and what specific assertion are you addressing?

This
Finally, it could be true that:
Our theory of black holes is not correct, they don't exist as we currently conceive them
Entropy for the black hole replacement in the new theory scales as r^3
and also why AS can't be right.

Well, it is only the last of four items. I don't consider it the most likely that's why it is last.

It remains nevertheless a possibility. If someone were to propose a specific theory at some time in the future that had this trait then it would be incumbent upon the authors of that theory to address the issues with respect to QFT that you have shown.

As Tom pointed out earlier:
In GR a black hole is a curvature singularity with an event horizon hiding the singularity from the outside oberver. One can calculate its temperature and entropy using classical GR with a semiclassical approx. for QFT. In LQC the curvature singularity is replaced by a mathematically well-behaved region w/o any singularity, whereas in full LQG the event horizon enclosing the singularity seems to stay intact. So the interior which no longer contains a singularity is still hidden from the outside observer.
So we have different theories predicting different ideas about what a black hole is. My earlier point that this means that we can't necessarily rule out behaviors which are predicted by GR stands. Let any given theory of quantum gravity deal with black holes as it may. As long as it is internally consistent, deals with the correspondence principle and can explain more than GR and quantum mechanics alone, it will find some success.

As to AS? I don't know enough about it specifically to offer even a modest assessment.

The issue of whether or not gravity is emergent or fundamental is orthogonal to the issue of black hole entropy being a function of area. That was the real focus of this thread. Black hole entropy is why holographic dualities are of interest because they solve the problem in one plausible way.

There are other ways that can address black hole entropy without relying on holographic dualities and some of these ways include the idea that gravity is fundamental.

tom.stoer
So we have different theories predicting different ideas about what a black hole is.
No, not really.

We know tat GR breaks down at or near the singularity and has to be replaced by something which is mathematically consistent.

LQG seems to do the job, unfortunately it is too complicated to solve all equations and one has to use approximations. LQC is (in a certain sense - please don't mess up my argument with minor details) such an aproximation. It predicts the elimination of the singularity but is unfortunately not able to talk about entropy of the gravitational degrees of freedom because it reduces the theory to only a finite number of them - which means that it has nothjing to say about entropy.It's a kind of toy model for full LQG - but a rather interesting one as it discusses exactly the same limiting cases as the spherically symmetric Schwarzsschild black hole and the spherically symmetric spherically symmetric scenarios.

Full LQG is too complicated to discuss the full dynamics, but one is already able to derive some quite interesting results, namely entropy via nearly exact counting of states, and the quantum geometry of the horizon.

So we do not have three different theories, but theories which are related to each other by taking the classical limit (GR from LQG) and by symmetry reduction (LQC from LQG).

Please note that in LQG the horizon degrees of freedom emerge automatically and need not be introduced by hand. Therefore the holoraphic principle is somehow emergent as soon as one studies a boundary between too regions of spacetime.

Thanks for the clarification tom.

atyy
This

and also why AS can't be right.
I understand your argument about the scaling of entropy, and agree that it is unclear how AS will solve it. Nonetheless, it is not clear that AS cannot solve it.

What do you make of this statement http://golem.ph.utexas.edu/~distler/blog/archives/001585.html ?"In any case, the existence of a “quantum” conformal symmetry in quantum gravity is compatible with there being a nontrivial dimensionful scale in the theory, so I don’t see a-priori why it’s incompatible with blackholes."

A second question is, is it clear in AdS/CFT, that if one runs the renormalization flow from high energies to low, that there isn't an IR fixed point in the full theory that would be a UV fixed point in gravity?

tom.stoer