Of Particular Significance

Physicists Discover String Theory and Extra Dimensions in a Laboratory!

POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON 12/05/2022

With a headline like that, you probably think this is a parody. But in fact, I’m dead serious. Not only that, the discovery was made in the 1960s.  Due to an accident of history, the physicists involved just didn’t realize it back then.

That said, there are profound problems with this headline.  But the headlines we’ve seen this week, along the lines that “Physicists create a baby wormhole in the laboratory”, are actually WORSE than this one. 

It is more accurate to say that “string theory and extra dimensions were discovered experimentally in the 1960s” than to say that “a baby wormhole was created in a lab in the early 2020s.” 

And now I’m going to show you why. As you’ll see in this post and the next, the two claims are related.

The First Gasp of String Theory

In the 1960s, a wide variety of “hadrons” (particles containing quarks, gluons and anti-quarks) were discovered — not just the protons and neutrons from which we’re made, or the pions and their cousins found in the 1940s and 1950s, but a whole host of them, with an alphabet-Greek-salad of names.  Study of these hadrons led to the proposal, prior to the discovery of quarks, that maybe hadrons are little strings.  There was quite a bit of experimental evidence for this idea! But to make a long story short, the proposal eventually failed when quarks were discovered and confirmed in the 1970s. (Meanwhile string theory was repurposed for a theory of quantum gravity etc. [a “Theory of Everything”], and the rest is history/not even wrong/lost in math/not even close.)

But actually, string theory didn’t fail.  It was just string theory in flat four dimensions that failed.

Bear with me. This takes a few steps.

String Theory and Quark/Gluon Theories Meet Again

In 1997, Juan Maldacena, following on old ideas of Gerard ‘t Hooft and Alexander Polyakov, among others, and hinted at by works by many other string theory/black hole researchers (such as Igor Klebanov, Andy Strominger, etc.), uncovered strong evidence for a radical conjecture:

  • There are quantum field theories (theories of gluons, quark-like particles, and some additional friends, but with no gravity, in a world with three space dimensions and one time dimension) that are exactly equivalent to supersymmetric string theory (a theory with nine space dimensions and one time dimension, with an infinite set of particles and fields, and with quantum gravity) where the strings are moving on a uniformly 9+1 dimensional curved space.

[[If you don’t know what “supersymmetric” means, don’t worry about it; it won’t be relevant here.]]

This sounds crazy at first. How can a theory with quantum gravity be equivalent to one without quantum gravity?  and how can two theories with different numbers of space-dimensions be equivalent? Nevertheless, the conjecture is almost certainly correct. In this post I won’t go into the mountains of evidence here in favor of this “AdS/CFT” or “gauge/string duality” conjecture. [A figure illustrating this relation, and some of the others mentioned below, is located at the end of this post.]

Within a short time, Maldacena’s conjecture was extended to theories that are more similar to the real world — gluon/quark/etc. theories that exhibit remarkably real-world-like behavior. This includes formation of hadrons out of gluons and quark-like particles, for instance, along with many extra hadrons not found in the real world.  The conjecture implies that these theories (not necessarily supersymmetric themselves) are also exactly equivalent to a supersymmetric string theory, with quantum gravity, but now on a more complicated curved space.

What makes this equivalence possible? The point is that even though the string theory exists in nine spatial dimensions (plus one time), only three spatial dimensions extend out to infinity and are visible macroscopically. The rest are somewhat curled up microscopically, but in a very clever way that assures that one of those dimensions is particularly long and important.  [See the figure at the end of this post for a rough illustration.] That long but finite fifth dimension — let me call it the “radial” dimension (the one that stars in the famous work of Lisa Randall and Raman Sundrum, which came soon after Maldacena’s conjecture) — is the one that assures this string theory has properties similar to the real world.  What are they?

  1. Unlike the string theory first considered in the 1960s, in which the strings moved on flat spatial dimensions, the curved nature of the space on which these strings move assures that none of the hadrons predicted by this new string theory arrangement should be massless [except possibly some pion-like particles.]
  2. For each hadron of low mass (M) and low “spin” (angular momentum J) there should be an associated set of hadrons of ever-increasing angular momentum and mass, with M growing roughly like the square root of J. [[These sets of hadrons are called Regge trajectories.]]
  3. For each particle of low M and low J, there should be a “tower” of hadrons of increasing M but the same J. [[These sets of hadrons are called Kaluza-Klein (KK) towers.]]

The precise details depend on the particular theory.  But these general properties — no massless hadrons, and hadrons organized into Regge trajectories and KK towers — are the basic predictions that are almost independent of any details. 

Well, long before this, when people discovered the hadrons of the real world, they learned that the quark-antiquark  hadrons (the “mesons”) of the real world do indeed satisfy all of these criteria.  (The baryons — hadrons like protons and neutrons — do too, but their story is more complicated and I won’t cover it now; there’s a little discussion here.) The real world has hadrons in Regge trajectories and KK towers, none of them massless. Nowadays we understand that this is the signature of a string theory with an extra finite radial dimension of space. The details of the hadrons teach us, in principle, the details of this string theory and the space on which the strings move. 

And so it’s completely clear, in hindsight, that the particle physicists of the 1960s discovered string theory and at least one extra spatial dimension, though they didn’t know it at the time.  (It’s even clear what quarks and gluons are — they are spikes on a string that nearly reach one edge of the radial dimension.) It was only after Maldacena’s breakthrough that this became self-evident.

In short, as physicists at the Large Hadron Collider and its many predecessors have been studying the physics of quarks and gluons and the details of hadrons, they have secretly been studying string theory, extra dimensions, and even (to a more limited extent) quantum gravity.

Surely You’re Joking, Mr. Strassler!

Now, many of you will be screaming bloody murder at the spectacular claims made in the two previous paragraphs.  And well you should be!… just as you should be screaming even louder at anyone claiming to have made (or even simulated) a wormhole in a laboratory.

The thing is, though, I’m not joking. The claims made in the previous paragraphs are both

  • factually true if Maldacena’s original conjecture is correct, and
  • morally/ethically outrageous for having left out all sorts of crucial fine print. 

By comparison, the claims made about the “lab baby wormholes”, which also rely on Maldacena’s conjecture, are suggestive rather than factually true, and the fine print is more extensive.

So let’s look at the fine print for the hadrons representing a string theory. I’ll need it when I come to wormholes next time.

The Fine Print About Hadrons, String Theory and the Extra Dimension(s)

I have to emphasize that it is absolutely true — if Maldacena’s conjecture is correct — that a theory of quarks and gluons found in the real world is exactly equivalent to a string theory in extra dimensions.  Take the real world and ignore its gravity (that would greatly complicate the story.)  Though it would be hard to carry out in practice, you could take one of Maldacena’s examples where the equivalence is well-established, add a few things to it (including the weak nuclear and electromagnetic forces and the Higgs field and electrons etc.) which maintain the equivalence, and then start stripping things away [via mass terms and expectation values] until you are left with the quarks and gluons of the Standard Model, and no remnants from supersymmetry or anything else the real world doesn’t have.  None of this messes up the equivalence.   There *is* a string theory in extra dimensions that is exactly equivalent to the real world.

Finding exactly the best way to construct this string theory, beginning to end, would be tedious and hard. To my knowledge, no one has even bothered to try. Why not?

The problem is that stripping out all that extra stuff, to move the theory toward the real world, is guaranteed to dramatically and qualitatively change the space in which the string theory travels.  It will become so tightly wound up and complex that it’s barely a space at all.  We don’t know any details of what this space looks like, except that, for sure, the long finite radial dimension in the cases described earlier becomes a very short radial dimension.  [See the Figure at the end of this post.] No one has any idea how to calculate anything about string theory on such a space [especially with “Ramond-Ramond background fields”, which make things infinitely worse], and so, no one can be sure how it actually behaves.   It’s not even obvious there should be any objects in the theory that intuitively resemble strings at all!

In fact, the only reason to be confident that this string theory actually has the characteristically stringy and extra dimensional features listed in (1), (2) and (3) above is that we have simulated this theory in a laboratory! In many laboratories, in fact. That’s what our particle physics accelerators that make hadrons have been doing for sixty years.  You see, from this perspective, the real world’s quarks and gluons, as observed in real-world particle physics experiments, can be viewed as a natural quantum computer simulation of this equivalent string theory, about which we otherwise know very little.

If theorists knew in the 1960s what we know today, the string theory interpretation of the data wouldn’t have been dropped so quickly. It would have lived on, well into the 1970s and 1980s and beyond. The competing views — quarks/gluons vs strings-in-curved-extra-dimensions — would have been seen as complementary, as they are today. But the required string theory is a heck of complicated beast, while the mathematics of quarks and gluons is, by comparison, very simple. Quarks and gluons are a much better intuitive basis for understanding the world, and allow us to make precise calculations for experiments, while the string theory, though it is of intuitive value in numerous contexts, is useless for precise calculations. (Admittedly, this is a technical problem, not a conceptual one. It’s conceivable that someday a mathematical breakthrough, perhaps one that would allow us to simulate string theories on an artificial computer, will make the string theory viewpoint more practically useful.)

[Extremely Important Caution: none of what I’ve said here implies that the string theory I’m referring to is a “Theory of Everything”. The string theory in question has nothing to do with the quantum physics of the gravity that holds you and me to the floor. Remember, this string theory is equivalent to quarks and gluons without gravity. To extend the story, so that the string theory’s gravity and our familiar gravity are one and the same, joined together in a seamless way, is possible (see here). But there is zero experimental evidence that this extension occurs in nature.]

Where does this leave us? We have learned from natural simulation that, for some reason we don’t understand deeply, the very complicated quantum string theory that’s equivalent to the real world’s quarks, gluon and hadrons has some remarkable, surprising, qualitative, but experimentally relevant similarities with the string theories that show up in the context of Maldacena’s conjecture, which aren’t the real world but whose properties can be calculated. Because of that, one can hope to learn some qualitative lessons about the real world using this equivalence (as many authors have done, including myself here and here.) This is a classic technique: consider a universe similar to ours in which you can draw a clear conclusion, and then hope/pray that you can draw a similar qualitative conclusion about our own universe. It works sometimes, but by no means always. You need more evidence, often from experiment, before you can be sure that your conclusion is valid in the real world. But still, even when you’re not sure of it, a plausible conjecture can occasionally point you to even better ideas.

Final Point for Today; Stay Tuned For More

Now, what about those wormholes? They rely on the same Maldacena equivalence, and they suffer from the same fine print, plus a lot more. (For instance, the wormhole that’s been quasi-simulated exists in only one spatial dimension, not three.) I’ll start to tell you their story in my next post.

In the meantime, let me reiterate: it is less true that wormholes (even baby ones) have been made (or even simulated) in a lab than it is that particle experimentalists of the 1960s discovered string theory and extra dimensions. Theorists in this subject have all known about the string theory viewpoint for the last twenty years or so, and we use it often, but we didn’t make a big deal out of it to the world’s journalists. Why not? Because the quarks/gluons viewpoint on the real world is both intuitive and practically useful, while Maldacena’s equivalent theory of strings on a tightly curved space is often neither, not to mention imprecisely known.

But hey, if physicists and journalists are all collectively going to lower the bar and make an international spectacle about a quasi-simulation of a cartoon of a wormhole, then, well, by that standard, I guess we ought to let everyone know that string theory and extra dimensions are absolutely real and have long been the subject of 20th- and 21st-century particle physics experiments. That’s no parody, no joke, no kidding. But don’t misread it for something more than it is. READING THE FINE PRINT ISN’T OPTIONAL!

Depiction of Maldacena's conjecture connecting string theory and field theories of quarks and gluons, in three different contexts.
(Left) Quarks, gluons and other particles that roam free in three dimensions [two of which are illustrated in the grey square], without forming hadrons, may be exactly equivalent (according to Maldacena’s conjecture) to strings moving on a nine dimensional shape, of which two of the usual dimensions and the most important extra dimension, the radial dimension, are shown. The space is empty and infinite; the orange slabs shown are imaginary, not physical objects, representing squares cut into the space along two ordinary dimensions, and spaced equally in the radial dimension. The grids on the square illustrate that distances are measured differently at different radial positions, indicating that the overall space is curved. The curvature is weak (i.e. the space isn’t far from flat) compared to the size of a typical string (sketched in dark red.) Strings may be found anywhere in the space but tend to fall. (Right) In cases where the quarks/gluons/other particles form hadrons, the radial dimension is finite; the space has a “floor” where strings are most often found. Crudely speaking, these strings-on-the-floor are the physical hadrons. In certain unrealistic cases, with many more types of hadrons than in the real world, the space the strings move in may be weakly curved and many things about the string theory can be calculated. But in the real world, the corresponding string theory is on a strongly curved space with a very short radial dimension; calculations of the details of this string theory are not technically possible with current mathematics. For this reason, we don’t learn anything precise or new from the existence of this string theory that we didn’t know from the quarks and gluons. Still, we can make lemonade from lemons, and take the point of view that studying hadrons in our particle accelerator laboratories teaches us about this string theory, much as one might use artificial simulations to learn about, say, wormholes.

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25 Responses

  1. I am puzzled by the term “Wormhole”. All relevant pictures I can find do resemble the (JoJo) Diabolo, which dates from 4000 – 30000 years BC. Real wormholes, at least the ones I know, don’t look like that.

  2. Professor, analyzing the 2 articles “Quantum Gravity in the Lab” and “Wormhole Dynamics on A Quantum Processor”, that is impossible to give reasons or to say if they are correct, because from using computation in those experiments, they must need transmit us their source code, base code, their program for everyone to know what they treat, to find errors in the programs. I say this as programmer. An example in programming, just from movies, special effects and even animations from Mickey, for example, the programs should be perfect to give it good movements, on highest mathematic propertys, equations of more than perfect movements, with realistic animation, better moving that the humanity can do it, like the Jurasic Park movie, but never they come true. We cannot confuse fiction, also extreme perfections, with reality. In computers, with high programming and equations, I can make an elephant flying (Dumbo?), But not so it becomes real. You see, I speak of the highest and current computation experiments, perhaps much more advanced than these phisics experiments. Therefore, the articles fail in not show us the source code. PS: I just talked about computation and never talk about physic theories. Can I be wrong? Yes, but I ask to refer me where. regards.

    1. I think the full code is probably given in a combination of equation (3), figure 1c, and the “Supplementary Information” which is available from Nature. In any case I’m sure the authors would provide it if requested. I will add that the authors include some of the most reliable and brilliant scientists in the field, and a mistake in this context is very unlikely (though of course all such efforts should be confirmed.)

  3. Using the duality for quarks/gluons and dumping the gravity portion of superstring theory, the other problem still remains that we don’t live in Anti De Sitter space, yes? You’ve mentioned (admirably too with your extreme caution comment) that the superstring language dual isn’t always the most useful to do calculations and also that you have to ignore large portions of it that *don’t* track with observation. Shouldn’t you also mention that one of those is that it is talking about Anti De Sitter space which we don’t live in?

    1. I didn’t mention it because it isn’t a problem. I’m not dumping the gravity from string theory, I’m keeping it. The duality has nothing to do with getting rid of the gravity in the superstring theory… only *our* gravity. I was relating 3+1 dimension quarks/gluons in flat Minkowski space to string theory in an 4+1 (+5) Anti-de-Sitter (x X) space. What’s the problem? My whole point is that we aren’t doing a theory of everything in which string theory explains the gravity we know, so it’s irrelevant what space the string theory lives in; it only matters that it’s equivalent to the quark/gluon theory.

      Conversely, if we *do* want to explain the gravity we know, using superstring theory, then again it’s not a problem… at least, not the way you seem to be thinking. That’s the point that Randall and Sundrum (and also Hermann Verlinde) made in the two papers I cited. The required space is an AdS throat glued on to a standard string compactification; the four-dimensional physics looks perfectly flat.

      However, if you want it to be slightly de Sitter, as it ought to be to describe the real world, that starts a whole long discussion about whether string theory can even have a stable de Sitter space, and whether our world, if described by string theory, must be unstable. This would take us far outside today’s conversation and I’m in no mood to go there today; suffice it to say that this leads to the whole discussion of the string landscape and I can’t tell you which of the many statements made in that context are actually correct.

      1. Einstein’s notion, from which all of your de Sitter and anti-de Sitter spaces ultimately derive, namely that time is a dimension and that we live in a spacetime continuum of some sort, is falsified by the simplest and most fundamental of the physical relations, i.e., s/t. In this relation, which we experience every time we measure movement of any kind, time enters the equation as the *reciprocal* of space, *not* as a dimension in addition to those of space. In short, vectorial motion is not s+t, but s/t. Since the space with which we are familiar has three dimensions, it seems not unreasonable to assume that the reciprocal of space (that is, time) is also three-dimensional. Combining each of the three spatial dimensions with one of the three time dimensions gives us three dimensions of motion. Has anyone, besides D. B. Larson and the few researchers following in his footsteps attempted to build a general theory on this foundation? For a century the most brilliant minds and untold wealth have been dedicated to constructing a model based on Einstein’s notion that time is a dimension. Could it be that the acknowledged failure to succeed in this endeavor is due not to a lack of ingenuity on the part of the researchers or to a scarcity of funds dedicated to the effort, but due to a defective premise? Would it not make sense to devote a tiny fraction of this gargantuan effort to an exploration of the notion that time is in fact a reciprocal of space, a mirror image thereof, as it were, this being what the only observable relation between the two, i.e., motion, unequivocally implies? The Ptolemaic system likewise failed, despite the collective effort of the best minds and a millennium of effort, due to a similar defect in its fundmental premise.

        Our perspective on things is distorted by the vast disparity in the units we use. The MKS system, which has been adopted because it is commensurate with human experience, uses as its basic units a meter, a kilogram and a second. Yet for the purposes of the fundamental speed defined by the s/t relation, the speed of light, a second is equivalent not to one meter, but to nearly 300 million meters. Conversely, a meter is equivalent to one 300 millionth of a second. This seriously distorts our ability to intuitively understand time in the same way we intuitively understand space. That time is something other than a dimension is evident from the fact that our familiar spatial dimensions are interchangeable. Rotation will turn axis y into axis x and axis x into axis z. But no amount of rotation will turn any of these three axes into axis t. By using a different notation for the time axis, such as 3+1, 4+1 etc., you are in fact acknowledging that “dimension” t is in some way different from the remaining ones.

  4. That was Wigner’s assessment of the situation, not mine. I only used it to illustrate the frustration of top physicists faced with observations that appear to defy any reasonable explanation. My own view is diametrically opposite. I hold that the universe is rational and the human mind capable of understanding its basic operations. Wigner’s exact words, to the best of my recollection, were: “I once tried to teach my dog the little table of multiplication. And a dog is very intelligent animal. But I did not succeed.” Checking my notes, it was at a conference at the Vista Hotel in what used to be the WTC, held on January 21st to 24th, 1985. The recently-completed Aspect experiment was the main topic of dicussion.

  5. What I find amazing is that despite an immense international effort stretching over many decades by some of the world’s leading intellects, the structure of the physical universe is still a guessing game. Even so fundamental a value as the number of dimensions remains a matter of conjecture. The status of time as a dimension is asserted without explaning why it operates quite differently from the remaining spatial dimensions, while at least one of the spatial dimensions is said to be more equal than the rest. Could it be so, as Eugene Wigner once told me at a QM conference in NYC (with his grave Hungarian accent that lent his words so much weight), that humans – although very intelligent creatures – may be as incapable of understanding QM as a dog – also a fairly intelligent creature – is incapable of learning the multiplication table? Or is it rather the case that a correct answer cannot even in principle be derived from erroneous premises? Wigner is, by the way, responsible for inventing the strong force to explain why the atomic nucleus is stable in the presence of positive charges in close proximity, essentially an “epicycle” that saved the Rutherfordian atom. But at what cost?
    I would like to bring your and your readers’ attention to the recent reprint of D.B. Larson’s The Neglected Facts of Science, available on Amazon, which establishes, based solely on empirical evidence, the existence of three dimensions of *motion* (rather than of space), in each of which space and time interact not as separate dimensions, but as reciprocals (which is how motion itself is defined, s/t being a reciprocal relationship). This implies that time is a three-dimensional entity equivalent to space, rather than being itself a dimension, as claimed by Einstein. Our spatial reference system is capable of representing only one of the three dimensions of motion. Furthermore, being by nature Cartesian, it represents all motion as velocity (i.e., a vector), even if the fundamental motion is non-vectorial, having no inherent direction. The directions within the Cartesian reference system are thus assigned to the fundamental motions arbitrarily by the observer. I need to proceed no further, I think, for the reader to understand how this addresses one of the fundamental problems of QM.

    1. I wouldn’t make much of Larson’s book.

      However, on your first paragraph, I agree that there is no guarantee that human intelligence is sufficient to fully understand the workings of the universe — and even less so, to understand something as complex as the brain itself. We will hit our limits eventually, but we don’t seem to be near them yet.

  6. Well, my previous comment was a bit premature, perhaps suitable for a subsequent post.
    Many people ( that are working actively on this correspondence) insist that not only it is “complete” ( in the sense that everything happens in the bulk has a corresponding description on the boundary, and vice versa), but the bulk description ( and spacetime geometry) emerges from a description that does not contain gravity at all. This is a much stronger claim, compared to your somehow more restrained blog post.

    Anyway, my previous questions have to do with my interests, so if you consider them irrelevant ( at least for a particle physics- focused blog post) I’ll understand.

    1. The conjecture is that it is complete. There is no evidence that the conjecture is wrong in any detail, and a lot of very concrete and complex evidence in its favor. My personal feeling is that it is correct, having computed all sorts of complicated variations on it and never encountered anything the slightest bit problematic. My blog post may have been restrained, but I have every reason to agree with the strong claim.

      And yes, the bulk description **must** emerge from a description with no gravity at all. Otherwise the conjecture makes no sense. You cannot have a four dimensional quantum theory equal a ten dimensional quantum theory unless one of them has quantum gravity, pushing all observables to the four-dimensional boundary.

  7. This is delightful!

    My focus on superstring origins has always been on 1974 Scherk and Schwarz [1] and others. They preceded 1997 Maldacena by a quarter century, so to be honest, I never thought to consider Maldacena as anything more than a much later elaboration.

    In his Nobel Lecture [2], David Gross gives a delightful history of his struggles in that period with the S-model and the focus then on “pure math” models of reality. To quote Gross:

    “Field theory was to be replaced by S-matrix theory; a theory based on general principles, such as unitarity and analyticity, but with no fundamental microscopic Hamiltonian.”

    S-matrix is important for understanding the origins of superstrings. Without the S-matrix insistence on a pure-math core to reality at its lowest levels, the extension of the hadronic strings model to encompass gravitons requires entirely new asymptotically free force at the _Planck_ scale (!), plus some new set of particles (!!) bound by that force to emulate the flux tubes and quark masses that produce the lovely Regge trajectories at the hadronic levels.

    Without S-matrix, that’s just silly. Saying that just because gravitons are spin-2 and the Regge trajectory transitions are spin-2 that they _must_ use the same mechanism transforms, without S-matrix, into postulating an almost exact analog of the strong force at energies 20 orders of magnitude higher, just to “explain” gravitons that themselves remain speculative to this day.

    I understand the enthusiasm of the time. Folks went ballistic at the possibility that those lovely Regge trajectories were revealing some deeper reality, and the hypothesis was worth exploring. But that was when S-matrix ruled the roost, and the quarks-plus-flux-tubes model was still hotly debated. Hadronic string vibrations lose an enormous share of their “magic” after they become not much more than the dynamics of quarks bound by flux tubes with asymptotic freedom, which in turn become simply the smallest examples of string-like systems supported by the Standard Model.

    Again, it’s hard to see how Maldacena is even relevant. His ideas didn’t pop up until the belief that “strings are simple” was so entrenched that brains didn’t stop to examine the idea anymore. The sad truth is that (a) strings are not simple, and (b) string vibrations are not simple. The strings and their vibrations encompass extremely complex force-based classical concepts such as tensile strength that seem trivial in the classical world but become harder to implement as you pare back the available ingredients. That’s why I love hadronic strings: They encompass the simplest possible model of “strings” and “string vibrations” that reality seems to make available to us.

    With all that said, I look forward to looking at your excellent defense of Maldacena more closely in the next few days.

    [1] J. Scherk and J. H. Schwarz, Dual Models for Non-Hadrons, Nuclear Physics B 81, 1 (1974).

    [2] D. J. Gross, Nobel Lecture: The Discovery of Asymptotic Freedom and the Emergence of QCD, Reviews of Modern Physics 77, 3 (2005).

      1. I don’t doubt Maldacena has done superb work and extremely cogent work!

        I’m no physicist, I’m a debugger. When a system locks up and stops producing actionable results — when it becomes code for code’s sake no longer produces actionable solutions, I look for root causes. That means going back to when the problem _began,_ not the noise generated by the problem downwind.

        The root issue here is simple and very much a physics issue: Do you accept that an empty vacuum has enormous and entirely real information storage capacity?

        If you do, give an example. Show how to store and retrieve real data from an empty vacuum, and make the _amount_ of data stored independent of local mass-energy.

        Do that, and you’ve enabled not only superstrings, but MWI, infinitely dense vacuums (you might want to _avoid_ that one, heh!), and even Deutsch and Marletto’s constructor theory. That last one is perhaps the most honest since it assigns infinite data storage and infinite _computation_ at infinitesimal points. Space becomes a matrix of computational deities who must confer with and constrain each other to create reality.

        Superstrings are no problem if you accept infinite or near-infinite free data storage and retrieval. Sure, they look insanely classical if you stop using abstractions and dare to ask, “what are they made of, exactly?” but with infinite information, you can create entire universes down there. You can postulate new particles — heh, rishons come to mind! — and bind them with new forces.

        But if Maldacena or others want to propose superstrings and claim they are a direct extension of hadronic strings, _please be explicit about what superstrings are composed of_. Hadronic strings make well-defined use of particles and fields to construct their vibrations and involve no handwaving as to the underlying physics.

        But all that assumes infinite data in the vacuum. What happens in real experiments if you try to store data in a vacuum?

        It’s not complicated: If you have mass-energy in the region, you can store and retrieve data in direct proportion to the total mass-energy in that region. If you don’t — if you are looking at instead Einstein’s perfectly frame-independent vacuum with no particles or fields — you get exactly zero, zip, nada information storage. Surprise, surprise: The vacuum behaves _like a vacuum_ when assessed for data storage.

        “But superposition! QED! Best theory ever!” Yes, but _none of that involves real data storage and retrieval._ QED calculates probabilities, that is all, and does so by _assuming_ point particles are the only way this probability estimation code can be written. That’s never true. All codes — all equations — have transformations that make them more efficient. Forcing code to _begin_ with the same point-like particles that quantum mechanics say are impossible is exceedingly unlikely to be the structure. The alternative is generative code — a restructuring of the same theory that gives the same results but uses conservation rules to drive the emergence of the same paths that make QED work so well.

  8. My question(s) : Is the conjectured correspondence exactly correct? To elaborate a little, does *everything* inside ( in the bulk) has a CFT description on the gravity-less timelike boundary?
    To be even more specific ( focusing on things that I’m mostly interested): What about the interior of an AdS black hole, i e. is there an inextensible ( in the Penrosian sense ) singularity in the future as in the classical theory?
    Among string theorists, G. Horowitz has suggested that in some cases at least, singularities are still unavoidable, even in the AdS/ CFT ( but that was a few years ago…)
    And what about more realistic rotating (or charged ) black holes ( that develop this very interesting “mass inflation” (*) instability in the vicinity of their inner horizon? Is there any dual description?
    [ (*) No relevance with the Cosmological term.]
    I have seen some papers that investigate mass inflation in AdS black holes, but not in the context of AdS/ CFT.
    And , finally, what about the Hawking radiation influx? How it affects the interior of an AdS black hole and the instabilities in the vicinity of their inner horizon?
    I understand that I’m asking too much, but these are really interesting issues that have to do directly with what one expects from a promising framework about QG, so even some hints will be welcome.

    1. Some of these questions have been answered to a greater or lesser degree. If you look at Maldacena’s extraordinarily long and interesting list of papers, you will find some of the answers.

  9. Can I ask a very naive question? Your article seems to say the two formalisms (for want of a better word) are equivalent mathematically – but does that say anything about the reality of the situation? Is it that there are really quarks etc as far as we can be sure if anything, but this tool is still useful. Or is it that philosophically they are actually equivalent? Thanks!

    1. Nothing naive about the question. The question is: if you have two equivalent formalisms that give identical predictions for all experiments, then which one is “right”, or “true”?

      The issue already arises in Newtonian physics. We are all taught F=ma, etc. in first year physics, which imagines the world as made of objects acted on by forces which determine how the present evolves into the future. But then in later years we are taught Maupertuis’s least-action principle, which tells us that the world is governed by minimizing action between the current present and an imagined future; forces, from this perspective, are an epiphenomenon. Then there’s the Hamilton-Jacobi formalism, in which reality is governed by waves. Which is “true”? or “right”?

      There is no scientific answer to this question, since science involves comparison of predictions with experiments, nothing more. If you have two (or more) formalisms that both give identical predictions, then no experiment can distinguish them, and they are equally true/right/valid. Nobody promised there would be a unique interpretation of reality; and in fact, already from Newtonian physics, we know there won’t be one.

  10. Absolutely spot on, Matt! Holographic duality is a mathematical tool (a damn good one), but it has been sold much more than this!

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