After my colloquium at UC Riverside some weeks back, I was asked an important question I’ve been asked before, and no doubt will be asked again. The same question may have occurred to you given things I’ve written here about the subject of my research concerning applications of string theory (particularly, ideas from quantum gravity) to understanding (relatively) recent experimentally measured phenomena. (The technique of “gauge/gravity dualities”: See also the special Physics Today May issue with articles on all of this. I wrote about that here. It tells you some of what we can and can’t do with the computational technology, and prospects for improvement, etc.)
So the question is “Is it real?”. This is particularly referring to the black hole in the discussion. Recall, one computes properties of new novel liquid phases of matter (that seem to be closely related to what shows up in the lab) by using a toolbox that involves the equations of gravity, in a higher dimensional spacetime, and much of the thermal nature of the system is controlled by a black hole solution of those equations. So people want to know if that black hole is real. A version of the conversation is like this: (Imagine I’ve already introduced the technique, the higher dimensional spacetime, and the black hole…)
Q: Is there a black hole living in the lab somewhere?
A: No, it is in a different place in the extra dimension.
[Wait! Don’t run off, readers. Thinking about an extra dimension is easy. Your coffee cup is on the table, so it shares the same coordinates as the part of the table it is resting on, right? Horizontally, there’s a certain specific amount of left/right-ness and back/forth-ness needed to locate it. But don’t forget that there’s also some up/down-ness (height above the floor) needed too. It is a third dimension that fully locates the cup in its spot on the table. Now raise the cup straight up off the table a little way. It’s not on the table any more. How did you do that? You changed the up/down-ness in such a way that the cup is in a different place. It is off the table because it is in a different place in the extra dimension (height, in this case) that the table top does not care about. Same words (italicized) as for the black hole business up above. It’s no harder than that, conceptually.]
Q: Ah, ok. But do you believe that this higher dimensional spacetime you’re doing the computation in, along with the black hole you put into it to model the phenomena properly, “exist” somewhere? Are they “real”?
A: Ok, interesting question. Here’s an answer…
I got this question in a recent email, and my (slightly edited) reply is below. The short summary is that my answer is two-fold (1) I don’t know what “real” really means, and (2) We should not mix up our computational tools with the thing we are trying to describe (Nature):
[…] You ask if there is anything “real” about the computations or if it is a mathematical technique. I don’t know how to answer that, to be honest. Is QCD [quantum chromodynamics, the theory we use to compute properties of the strong nuclear interactions which quarks, for example, interact with] “real”? Ultimately, I don’t know what real means. You’re wondering about the black hole and the extra dimensions, I imagine. The pragmatic approach is that it does not matter what the nature of the wheels and cogs are going on in the background, as long as they work together to give sensible testable physics. We’ve seen this before. For example QCD has gauge invariance. Is that symmetry “real”. I would say no. Gauge symmetry is a symmetry of the formulation, not of Nature. Everything in the strong interactions is a colour singlet…. In other words, while the theory has red, blue and green quarks on the page, Nature could not care less about red, green and blue quarks, and so forth. Taken literally, there’s an entire internal space that QCD uses in order to work properly, mapped out by the freedom to move around using gauge transformations …. more technically, there’s an SU(3)’s worth of freedom at every point (an eight dimensional space)… But we don’t go around taking that space as seriously existing, although we could do so, along with a long explanation as to why we never see it directly. Same goes, in my opinion, for these gauge/gravity dualities. The gravity theory is a tool for getting the computation done. (There are phenomenological scenarios that use variants of gauge/gravity dualities, branes, and AdS/CFT to discuss extra dimensions and their measurable consequences (examples include ADD and Randall-Sundrum), but it can be thought of as a logically different issue, which I won’t explore further here.)
As for your question about my comment in the colloquium about the non-reality of SU(3) colour (not flavour), see above. This is no more profound than what we already know for electrodynamics. It is a U(1) gauge theory. Formulated in terms of potentials, there’s a freedom to write things in terms of potentials, up to an ambiguity – the gauge transformations. We can use that ambiguity to help our computations, but fundamentally, the physical quantities do not ascribe meaning to the gauge invariance. It simply isn’t there in the physics… it is there in the computational tool – electrodynamics. Same for QCD.
My main point is that it is important at every stage to not mix up our tools with the actual physics, as is so often done.
I hope that helps.
I could go a touch further on the issue of what “real” means if pressed. Let me save that for a possible followup post.
-cvj
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The quark-gluon plasma (or, more aptly, the N=4 supersymmetric gauge theory plasma) is what it is … whether you like it or not.
I am completely unable to parse what you have written (except for the vague impression that you don’t think the quark-gluon plasma is “fundamental” enough to merit studying). And I really did try …
Jacques,
Moshe said; “When discussing highly complex many-body and strongly fluctuating systems…”
Which part of many-body is not composite?
Moreover, you missed my point again. Kindly revisit what I’ve written.
Moshe was referring (in particular) to the quark-gluon plasma.
The AdS/CFT correspondence works equally well (indeed, that’s where it was first discovered) for the zero-temperature N=4 super-Yang-Mills theory. If working at finite temperature isn’t “fundamental” enough for you, would zero-temperature be better?
Jacques,
I apologise for being incoherent. Moshe wrote;
” When discussing highly complex many-body and strongly fluctuating systems (with both thermal and quantum fluctuations), you realize that lots of the structure you attribute to the system has to be dropped, because it is a property of certain approximations rather than a property of the system itself.”
This is what I had in mind though, from my perspective, Moshe has put it more vaguely. Particularly because he is discussing complex phenomena rather than – with all due respect – fundamental physics.
Clifford,
I agree that the notions of holography are more interesting I think for the physics rather than an alluring, seductive mathematics. However, being pedantic, by definition I would disagree by saying that they are less compelling. They are at the moment less than axioms.
“You are about to enter another dimension, a dimension not of sight and sound but of renormalization-group flow. . .”
</rod serling>
In other words, the same way you don’t attribute reality to different electron trajectories in the double slit experiment, you cannot generally attribute reality to things like location in the fifth dimension, or the number of gluons in your plasma. Unless your wavefunction is peaked around a certain configuration, which you then can call “real“. But in that sense, in the appropriate limit the fifth dimension has more reality than the number of gluons in the plasma, though it is probably easier to have a mental image of the plasma as being “made of” tiny billiard balls we call quarks and gluons.
I think that this question could be valuable one to contemplate, even beyond explaining our stuff to outsiders. When discussing highly complex many-body and strongly fluctuating systems (with both thermal and quantum fluctuations), you realize that lots of the structure you attribute to the system has to be dropped, because it is a property of certain approximations rather than a property of the system itself. Even in ordinary QM you know that you are supposed to avoid counterfactuals if you don’t want to get confused, but this goes well beyond that.
Hi Bill,
The five dimensional theory is a full theory of gravity, and so 5D Lorentz invariance is manifest in the general duality.
In working in the thermal theory in particular, we arrive at a particular background – there is a black hole. In having a background 5D Lorentz invariance is broken, but the 4D Lorentz of the radial slices (transverse to the black hole horizon) is preserved. This is the mechanical way of seeing why one direction is singled out over the others.
More generally, from the perspective of 5D, the full family of symmetries of course form the group isometries of the AdS space. One can look at how they appear from a four dimensional observer and they look like the 4D conformal group. Then, the part of isometries involving the radial direction are to do with dilatations/scale transformations. Indeed, from the perspective of a field theory, these are connected to energy scale in the usual way.
Put another way, think of every radial slice of AdS as a copy of the theory coarse-grained up to a given energy scale set by that radius. The coarse-graining/cut-off procedure is what we do in any field theory computation (either implicitly or explicitly), which leads us to the usual picture of RG flow, and so on and so forth. What AdS (more generally, any gravity dual) does for you is supply you with the entire family of slices of the 4d theory, one for each energy scale, all nicely ordered next to each other. Lining them up like this begs one to think of the whole things as 5 dimensional. Is there an economical writing – a theory – that controls this 5d picture? There need not be, you might argue, but maybe there is in some fortuitous cases… gauge/gravity duals are such cases: Remarkably, the higher dimensional theory of all those slices lined up next to each other turns out to be able to be written succinctly as something familiar: gravity. Perhaps, in retrospect, it _had_ to be gravity that can do this as it is really the only thing you can put there that does not have too many degrees of freedom propagating (4d’s worth, not 5d’s). Its holographic property is just what the doctor ordered here. (This last bit of reasoning about this way of thinking of gravity’s role here, making the whole thing nicely compelling, I picked up from a nice chat with Allan Adams.)
Cheers,
-cvj
“If it were real, then since the boundary is in full causal contact with it, we should be receiving signals from the bulk.”
No.
That statement stems from a rather oversimplified picture, suggesting that you have not taken the time to learn the setup under discussion. Might be worth familiarizing yourself with the properties of asymptotically AdS spaces before proceeding.
Best,
-cvj
I don’t believe for one moment that the bulk is real [and I make no apologies for refusing to put quotation marks around that word]. If it were real, then since the boundary is in full causal contact with it, we should be receiving signals from the bulk. Of course one can cook up reasons for why the bulk maintains radio silence, but it is simpler just to regard the bulk as a convenient mathematical fiction.
The fact that there is an exact one-to-one correspondence between items in the bulk and items in the boundary does not impress me. There is an isomorphism between the integers and the even integers; shall we conclude that odd numbers aren’t real? Or that odd numbers are “really” even numbers which aren’t multiples of 4?
Nice post Clifford, on a question that I have fumbled with on many occasions. I first encountered it a KITP workshop in 2004 on “QCD and String Theory”:
http://online.itp.ucsb.edu/online/qcd_c04/
But then, and now, my question didn’t focus on the reality of the black hole, but instead on a necessary precursor, that is, the reality of the extra dimension.
The 5th dimension in AdS/QCD plays the role of an energy scale, with distances in the 5th dimension getting converted to energies using the AdS curvature. We learn as undergraduates to become comfortable with adding a bit of time to a bit of distance in the Lorentz transformation. Is the 5th ‘energy’ dimension also allowed to participate in Lorentz transformations on the 5D side of the duality?
I think the answer is “Yes, in principle”, but the AdS/QCD set-up is such that the 5D metric shows a separation between the radial ‘energy’ coordinate and a Minkowski-like 4D piece, so that integrating over the radial coordinate in the action leaves you with a 4D flat space with interesting SU(N) gauge theory dynamics. I would of course be interested in your thoughts and/or corrections to these statements.
Claver,
I’m afraid that I cannot understand your comment. Perhaps that’s because you mean something different when you use the phrase “semiclassical configuration” than quantum field theorists mean.
Ah ok, thanks for your help, I’ll do as you say.
Jacques,
Respectfully. If we define reality, say the semi-classical configuration, as a consequence of the usefulness of its semi-classical approximation aren’t we missing the point?
The point being; we wish to derive a useful approximation from an observable semi-classical configuration. (Quite possibly, the restrictions imposed by the need for an observable configuration limit the methods of approximation.)
Moreover, if we have determined by experiment some semi-classical configuration, the consequent semi-classical approximation can be tested against this. Let’s label the semi-classical configuration a gedaken experiment.
Hence, let’s pose the question Prof. Clifford faces in another way; perhaps(perhaps) the gedanken experiments (semi-classical configurations) described in String theory do not provide compelling* restrictions on the possible semi-classical approximations?
*Compelling in the sense of accessible to experiment, something experimenters find compelled to test.
The answer, in lieu of unproven extra dimensions, landscape, supersymmetry…etc, would appear to be yes, the semi-classical configurations are not manifestly compelling. Not yet.
It is not possible to say that the Standard Model and General Relativity do not have compelling gedanken or non-gedanken experiments. Perhaps String theory should flow from unique and compelling gedanken experiments.
You’re confused by the use of the term “gauge” in “gauge bosons”, and assuming that requiring gauge invariance therefore removes them from the theory. That’s not correct. The terminology is misleading you. Let me urge you again to open a standard textbook on gauge theory at this point.
All the Best,
-cvj
Yes, I know about gauge invariance, physical results should be gauge invariant, but how does it help here?
Let me make the question more precise:
1. Photons are gauge bosons – quanta of a gauge field
2. Gauge fields are not physical (they are not gauge invariant)
3. From 1 and 2 it follows that photons are not physical
4. Therefore photons cannot be responsible for mediating EM interactions since those are physical – clearly nonsense
Obviously there is an error here somewhere but where? In 2? Are gauge fields physical?
Paul,
If the sources that you read don’t mention the key concept/principle of gauge invariance, I’d recommend using other sources.
Best,
-cvj
Hi Jacques,
Thanks. Yes, this is what I’m getting at when I say I don’t really know what “real” means. When you have a dual formulation of the the physics in new variables (the whole point of this business, as far as I am concerned) I don’t know what is more real than the other.So yes, the Yang-Mills theory is as real as the black hole…. or as unreal… take your pick.
On the other point, yes, some of the quark-gluon plasma’s behaviour is captured by the black hole setup in an approximation (I regularly remind people that there’s work to be done on this to better understand how far it can be pushed), but I think that even so, the question still stands. I think if you find variables that work really well in describing a problem, the question about whether they are “real” or not is going to come up. I don’t think it is so different from asking the question when you can even “prove” an exact duality…
Cheers,
-cvj
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Actually, I should make a caveat to the above remark (which ties into Moshe’s comment). Speaking about “the 5D blackhole” is speaking about a particular semiclassical configuration of the bulk theory.
Semiclassical configurations are “real,” only to the extent that the semiclassical approximation is a good one. Which is true, in this case, only in a particular limit (of large N and strong ‘t Hooft coupling). And, in this limit, the N=4 SYM theory isn’t remotely semiclassical (which was Moshe’s criterion).
I was taking the “5D blackhole” more figuratively to denote the bulk quantum gravity theory, which is “real” (but not necessarily semiclassical) for any value of the parameters.
I think the “real” question can be asked at two levels.
1. Is finite-temperature N=4 super-Yang Mills “really” a 5D blackhole?
The answer is “yes.” They are equivalent formulations of the same thing. Any sensible physical question you can ask about the one can be translated into a sensible physical question about the other. It may be easier to calculate the answer in one or the other formulation. But one is not “more real” than the other.
2. Is the RHIC plasma (or whatever your favourite application) “really” a 5D blackhole?
The answer is “no.” That’s just an approximation.
There’s all sorts of stuff about the real world that we are suppressing, even in saying that the RHIC experiment is described by a plasma (in quasi-equilibrium) and that RHIC plasma is described by QCD (neglecting, e.g., electroweak effects). Moreover, in replacing QCD by N=4 SYM, we’re making another approximation, based on the belief in the “universality of (certain) properties of strongly-interacting gauge theory plasmas.
But, once you’ve reduced the world to N=4 SYM, there’s no further meaning to the question of whether the AdS dual formulation is more or less real.
Are the solitons of Sine Gordon any more or less real than the fermions of the massive Thirring model?
Perhaps it was this paper?
http://arxiv.org/PS_cache/arxiv/pdf/1002/1002.3876v2.pdf
Verlinde’s Approach,
I was pretty sure I’d read a paper somewhere in the Forests of Arxiv that seemed to pop the balloon. I may be wrong.
I do think that the arguments presented in such a manner are slightly tenous. However, that’s probably the most clear explanation given by anyone that shows distinctly the state of String theory.
I daresay, perhaps Dr Clifford could develop that into a kind of axiom, ‘Shut up and calculate in the shadow of a blackhole’.
I say tenous because it’s always tricky trying to appropriate notions from QCD to justify notions in String theory. Rather than deriving them.
Is QCD real? Well, it really works. Not just aspects of it, but it’s entire mechanism is fit for purpose.
I keep encountering some variant of this statement – “Gauge symmetry is a symmetry of the formulation, not of Nature,” but it doesn’t seem to fit with other things I’ve read.
For example forces are said to be mediated by gauge bosons – quanta of gauge fields, but forces are definitely part of nature, a photon is part of nature we experience photons all the time.
Then there is U(1) gauge symmetry which is related to quantum phase but again quantum phase seems to be a part of Nature – we can clearly visualize it in a double slit experiment, we won’t detect particles where the phases of two paths cancel. So to me it doesn’t look like a part of superfluous formulation but rather like a crucial element of the formalism which dictates the physical outcome.
I would love to know how these apparent contradictions can be reconciled.
Hi Elliot,
I do not yet know what to think of the paper. I can say however that I also expect gravity to be emergent, since I think that spacetime is emergent and so its dynamics (gravity) ought to be too. The right mechanism is unclear to me, but I firmly believe that gauge/gravity dualities are important clues in all this (gravity apparent on one side, not on the other)… but whether the Verlinde approach is the answer, I do not know. If I have further thoughts on this paper worth sharing (I wish I did), I’ll let you know.
Best,
-cvj
Hi Excited State!
I’ll give another example in a followup post, but first…. what do you mean by SU(3) being “discrete”? I’m confused by that.
What you might be saying, in addition, is that the extra dimension here is quite dynamical, while in the gauge theory case they are not so. It is a distinction I see, but I don’t know how important that is in this. It is an interesting issue.
Cheers,
-cvj
I am doing some beginning work with AdS/CFT as applied to QCD, so I’ve gotten some similar questions from fellow grad students. I like your comparison to SU(3) color symmetry, and I may use that in the future. But there are a couple of differences that may or may not be important in regards to the question of “reality.”
First, SU(3) is a discrete space, which we do not have everyday experience with, so there is little risk of confusing it with “ordinary” space, once one gets used to the idea of abstract spaces.
But in this case, we are adding extra the extra dimension to our metric on a similar footing with the real dimensions of space. (Although there are important differences, such as a warping and a cut-off in my case.) I think this blurs the distinction between the dimension that is a mathematical tool and the dimensions that we experience.
Of course, we could say that the “usual” dimensions are also mathematical constructs, but I think that gets a little more philosophical than we need to worry about.
I look forward to your further thoughts on this issue.
Consider yourself pressed Clifford…
I’ve been meaning to ask you about your opinion on Verlinde’s paper:
http://arxiv.org/abs/1001.0785
which suggests that gravity is an entropic force and an emergent not fundamental property. In the context of what is real, this paper begins with assuming the reality of holographic scenario. So I think it is relevant to the discussion of what is real and what is not. If you take his thesis seriously, it may be that the holographic principle describes our reality and gravity is not a real thing but a by product of the change in positional information.
As you may remember I have speculated on the idea that positional information and gravity are intimately connected. (not sure if it was on this blog or elsewhere) but I am curious as to your opinion on this paper.
cheers
e.
Hi Moshe,
Yes, you do get a lot of grasping at the phrase “mathematical application” in this context especially from people who find the idea that string theory might be relevant to experimental systems runs up against their wish to believe or hope that it has nothing to do with Nature. It starts coming down to philosophy, personal tastes getting in the way, and so forth, and at that point I tend to start admiring the drying paint…
When does a tool for describing nature stop being a “mere” tool and become a “real” thing? Modern physics aside, consider even the case of calculus…
As I said, if pressed, I can say more about this sort of thing, but I’ll leave it for a followup post that I’ll do….. if pressed.
Cheers,
-cvj
You know, that is something I struggled with also. Not only when people invariably ask, or equally often make statements, about what is “real” and what is only “mathematical application”, but also when trying to make clear statements I believe in myself.
Provisionally, I think that a precondition to being “real“ in the sense people like, is being close to some sort of semi-classical limit. Ascribing reality to anything that is not close to being classical leads to all kind of confusions.
I like the thought also, because in this sense the 5dim black hole is more “real” that a bunch of “strongly interacting quarks and gluons“, which is a very bad description of what is going on in the plasma. Unfortunately, “real” can also means familiar or intuitive, and 5dim black hole in AdS is not that.
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