The Parable of the Entanglers and the Bootstrappers

There’s been some buzz around a recent Quanta article by K. C. Cole, The Strange Second Life of String Theory. I found it a bit simplistic of a take on the topic, so I thought I’d offer a different one.

String theory has been called the particle physicist’s approach to quantum gravity. Other approaches use the discovery of general relativity as a model: they’re looking for a big conceptual break from older theories. String theory, in contrast, starts out with a technical problem (naive quantum gravity calculations that give infinity) proposes physical objects that could solve the problem (strings, branes), and figures out which theories of these objects are consistent with existing data (originally the five superstring theories, now all understood as parts of M theory).

That approach worked. It didn’t work all the way, because regardless of whether there are indirect tests that can shed light on quantum gravity, particle physics-style tests are far beyond our capabilities. But in some sense, it went as far as it can: we’ve got a potential solution to the problem, and (apart from some controversy about the cosmological constant) it looks consistent with observations. Until actual evidence surfaces, that’s the end of that particular story.

When people talk about the failure of string theory, they’re usually talking about its aspirations as a “theory of everything”. String theory requires the world to have eleven dimensions, with seven curled up small enough that we can’t observe them. Different arrangements of those dimensions lead to different four-dimensional particles. For a time, it was thought that there would be only a few possible arrangements: few enough that people could find the one that describes the world and use it to predict undiscovered particles.

That particular dream didn’t work out. Instead, it became apparent that there were a truly vast number of different arrangements of dimensions, with no unique prediction likely to surface.

By the time I took my first string theory course in grad school, all of this was well established. I was entering a field shaped by these two facts: string theory’s success as a particle-physics style solution to quantum gravity, and its failure as a uniquely predictive theory of everything.

The quirky thing about science: sociologically, success and failure look pretty similar. Either way, it’s time to find a new project.

A colleague of mine recently said that we’re all either entanglers or bootstrappers. It was a joke, based on two massive grants from the Simons Foundation. But it’s also a good way to summarize two different ways string theory has moved on, from its success and from its failure.

The entanglers start from string theory’s success and say, what’s next?

As it turns out, a particle-physics style understanding of quantum gravity doesn’t tell you everything you need to know. Some of the big conceptual questions the more general relativity-esque approaches were interested in are still worth asking. Luckily, string theory provides tools to answer them.

Many of those answers come from AdS/CFT, the discovery that string theory in a particular warped space-time is dual (secretly the same theory) to a more particle-physics style theory on the edge of that space-time. With that discovery, people could start understanding properties of gravity in terms of properties of particle-physics style theories. They could use concepts like information, complexity, and quantum entanglement (hence “entanglers”) to ask deeper questions about the structure of space-time and the nature of black holes.

The bootstrappers, meanwhile, start from string theory’s failure and ask, what can we do with it?

Twisting up the dimensions of string theory yields a vast number of different arrangements of particles. Rather than viewing this as a problem, why not draw on it as a resource?

“Bootstrappers” explore this space of particle-physics style theories, using ones with interesting properties to find powerful calculation tricks. The name comes from the conformal bootstrap, a technique that finds conformal theories (roughly: theories that are the same at every scale) by “pulling itself by its own boostraps”, using nothing but a kind of self-consistency.

Many accounts, including Cole’s, attribute people like the boostrappers to AdS/CFT as well, crediting it with inspiring string theorists to take a closer look at particle physics-style theories. That may be true in some cases, but I don’t think it’s the whole story: my subfield is bootstrappy, and while it has drawn on AdS/CFT that wasn’t what got it started. Overall, I think it’s more the case that the tools of string theory’s “particle physics-esque approach”, like conformal theories and supersymmetry, ended up (perhaps unsurprisingly) useful for understanding particle physics-style theories.

Not everyone is a “boostrapper” or an “entangler”, even in the broad sense I’m using the words. The two groups also sometimes overlap. Nevertheless, it’s a good way to think about what string theorists are doing these days. Both of these groups start out learning string theory: it’s the only way to learn about AdS/CFT, and it introduces the bootstrappers to a bunch of powerful particle physics tools all in one course. Where they go from there varies, and can be more or less “stringy”. But it’s research that wouldn’t have existed without string theory to get it started.

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18 thoughts on “The Parable of the Entanglers and the Bootstrappers

  1. pete1187

    Great write up!

    I had a question related to the string vacua that you briefly mention in passing. I read on Motl’s blog a little while back that the 10^500 number may have been a colossal underweight, and in fact it’s closer to 10^272,000. Here is the link: http://motls.blogspot.com/2015/11/there-are-many-more-flux-vacua-in.html

    Just wanted to get your thoughts, as your my go to on questions related to string theory and fundamental physics.

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    1. 4gravitonsandagradstudent Post author

      Yeah, I saw that too. One issue with all of these counts is that it’s still a bit controversial which vacua are actually stable/realistic (the cosmological constant issue I briefly mentioned in the post complicates this, for one). The one thing people tend to agree on is that the number of vacua is very large and finite. While the new estimate is interesting, I don’t think it’s likely to be the final word on the story.

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  2. Giotis

    Why you are talking about failure as a ToE?

    Is it bizarre that a theory has many solutions?

    Is it bizarre that all these solutions can be realized in principle?

    No, of course not, quite the contrary it is the norm I would say.

    Also don’t forget that (excluding AdS/CFT) we don’t have a deep understanding of the theory at non perturbative level at least; this is still work in progress.

    Besides Gravity people often forget that String theory is the only theory that can produce and explain Yang-Mills gauge fields (another pillar of the physical world) from first principles.

    It is amazing that almost every deep insight of the physical world acquired during the last decades has been discovered and flourished within the general context of the theory and people are still talking about failure.

    We have a theory that keeps on giving and giving on one hand and on the other hand you have a dead theory like LQG which demonstrably badly violates reality (e.g. Lorentz invariance at low energies) and does not explain anything at all (you cannot even derive GR from it) which not only is not abandoned by its practitioners but shameless enough this carcass is promoted as a competitive alternative to String theory.

    BTW can you include RSS feed for the comments section too?

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    1. 4gravitonsandagradstudent Post author

      Failure as a uniquely predictive ToE. It’s still perfectly viable as an ultimate theory, sure, but the old dream of postdicting the electron mass, or predicting masses for low-energy SUSY, didn’t pan out, which is why people are no longer working on that particular project. 😉

      Non-perturbative understanding is sort of what I was gesturing at with the “entanglers”. There are other ways to get at it than via holography, but at the moment that’s one of the dominant ones.

      “Producing Yang-Mills from first principles” isn’t quite the way I would phrase it. After all, you can also “produce Yang-Mills from first principles” via fiber bundles. But the sentiment, that string theory is the only theory that explains gravity and Yang-Mills in terms of the same physical source, is a valid one.

      I believe wordpress provides ways to follow the comments, but I don’t know if there’s a widget to allow RSS. If there is, could someone tell me what it’s called?

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  3. Puzzled

    So string theory has been successful right? One think I could never understand about string theory is how is that we know everything we can get nothing? For example, when general relativity came about it made several distinct predictions that clearly differentiated it from any other theory of space-time that existed at the time. Mercury orbit, bending light, gravitational waves you name it.
    With string theory we should be able to know things way beyond that. Quantum gravity you name it. But there’s not one, not a single practical prediction that could clearly point to it being correct – or not. Accelerator energies are too low? Forget the accelerators there’s whole Universe with energies way beyond imaginable. Still too low? There’re black holes that bend space time to enormous levels where some quantum gravity effects should appear, There’re the mysteries of entanglement paradox, event horizon. So how would you explain the nature of this success that produces nothing – in real, practical terms for decades with tens of thousands of most talented folks working on it? I’m puzzled

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    1. 4gravitonsandagradstudent Post author

      It’s an issue of high energies, but also of small effects.

      Colliders are a no-go for obvious reasons, we just can’t get enough energy.

      With cosmology, you can potentially observe something, but you have to be sensitive to very small deviations from the norm, because even on that scale quantum gravity effects are tiny. So for example, BICEP thought they had observed quantum gravity effects, but it turned out they were caused by interstellar dust. And that’s just observing “something that looks quantum”, not even enough detail to distinguish rival theories of quantum gravity.

      Black holes have that problem, plus the issue that most of the interesting effects happen inside the horizon, where you can’t get information out anyway.

      There are potential sources of evidence about quantum gravity, but even the best of them are currently pretty vague. Maybe future successors to the BICEP experiment will be sensitive enough. Maybe someone will see violation of special relativity, which is predicted by some of the non-string quantum gravity proposals. Maybe LIGO or its successors will see evidence of cosmic strings. Maybe people will have some success using string theory as inspiration to suggest models for lower-energy physics.

      The problem here isn’t that string theory itself is bad at making predictions. It’s that quantum gravity in general is only at the barest edge of our radar right now, even with the most indirect approaches. That’s a problem for every quantum gravity proposal, not just string theory.

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      1. Puzzled

        Forgive me, but I’d have very hard time buying that with the most powerful theory in physics ever (success in quantum gravity, remember?) we cannot find one, single effect that could clearly tell us yes, you’re on the right track (or no, you are not) in all of the observable reality and regardless of amount of effort invested in the research. General relativity was a much more modest theory – it only dealt with one force and on the classic level, but it delivered several clear, distinct predictions not obvious but observable eventually, even if in a hundred years. Maxwell theory before then did the same. As many other theories in physics. And now we have this wonderful theory that explains everything but doesn’t point to a single, just one testable new effect? I’m sorry something isn’t right here. Just that it never happened before.

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        1. 4gravitonsandagradstudent Post author

          Quantum gravity itself is a weird field, because the problem it’s trying to solve isn’t experimental, it’s technical. If you naively put together quantum mechanics and general relativity, you get something that hasn’t violated any experiments…and can’t make any predictions. It’s a theory that’s mathematically broken, not one that disagrees with experiment, so the solution starts out mathematical in nature.

          General relativity was like this too, in some sense, but it’s the only example I can think of. Maxwell’s theory of E&M was built to explain Faraday’s observations, Newtonian mechanics to make sense of mechanical experiments and astronomical observations. In all of those cases, people were trying to theorize about something that was already experimentally accessible.

          Einstein was lucky to have something like the transit of Mercury that he could observe with current technology. For the most part, general relativity didn’t start being relevant to astronomers until the 60’s, until black holes were discovered and cosmology really took off.

          When you’re trying to solve a mathematical problem like that, there’s no guarantee that there are any nearby experiments to weigh in on it. That’s not exclusive to string theory, or to quantum gravity: there’s no experiment you can do to confirm in which dimensions the Ising model is exactly solvable either.

          Now, just because something is a potential answer doesn’t mean it isn’t a waste of time. And in some sense, it is. There’s very little point in just computing more and more corrections to the probability of two gravitons scattering if nobody is going to measure that probability. The thing is, though, that’s why people aren’t doing those calculations.

          The things that people kept working on? They’re the open questions, mathematical and physical. They’re the entanglers and the boostrappers, and all the other sub-groups working on all the other sub-questions. Absolutely nobody is sitting back and saying “well string theory explains everything, time to go to lunch”. We’re academics: it’s publish or perish out here.

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          1. Puzzled

            OK. I would then encourage you to think along these lines: let’s say you’re in that Planck world. So how would you know what is out there: those tiny string with extra dimensions, space-time foam, weird space-time connected triangles, etc? You will have to know that, right? They cannot be all there at once. This is where the experiment comes handy, to all the beautiful math that we can imagine. Then, if you know the answer, you can try to extend that understanding to other cases and environments maybe even outside of Planck. It would be pretty weird if our understanding of quantum gravity was cut out exactly by the Planck boundary and showed perfect agreement with classics everywhere else. It’s not impossible just rarely (never?) happened before as the slight and tiny effects from more advanced theories trickle hints for those who can see them. More specific? The entanglement paradox. Firewalls and event horizon. If we really had a consistent mathematical theory of the Planck scale shouldn’t we be able at least approach those questions? Otherwise the claim of string theory being successful would ring hollow to me, sorry.

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            1. 4gravitonsandagradstudent Post author

              Indeed, there probably would be indirect evidence above the Planck scale. But I think you’re underestimating just how far away the Planck scale is: we’re talking around twenty orders of magnitude beyond what we can probe right now. Even an effect substantially larger is still very very far away.

              Not sure what you’re referring to as “the entanglement paradox”, plenty of things under that name don’t have much to do with gravity. Firewalls in particular are very thought-experiment-ish, in the most common understanding they would only exist in black holes older than the current age of the universe. These really aren’t things that are any bit more experimentally accessible than the Planck scale itself.

              That doesn’t mean that there aren’t other indirect effects to find. But so far, not just string theory, but no quantum gravity theory has concretely proposed any. It’s not because everyone who works on the subject is being sneaky and hiding these sorts of things under the rug, it’s because there’s genuinely very little to find.

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              1. Puzzled

                OK, I’m making only one point here, really. String theory can be an idea, a framework, a line or domain of research, as much successful at that as you want to name it. But it will only become a physics theory after it will make at least one non trivial and verifiable prediction that would differentiate it from other theories. And a successful theory only comes after such a prediction has been verified by an experiment. Subscribing to anything less we risk to fall back to the times of ancient philosophers who had many beautiful ideas but had to take their refuse out in buckets due to lacking basic canalization.

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                1. 4gravitonsandagradstudent Post author

                  I agree on the substance.

                  I suspect a big part of what’s bugging you is the use of the term “theory”. Theoretical physicists use “theory” in a different way than how philosophers of science use it. For us, a “theory” is a complete specification of a way to set up a world, but not necessarily the one we live in.

                  String theory is a theory in that sense. It might, one day, be a theory in the philosophy of science sense, one with experimental confirmation and reliable predictions. But for the moment, it doesn’t have that kind of confirmation, and nobody is treating it as if it did. We’re treating it as a promising direction, not an established fact about the world.

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                  1. Puzzled

                    Great but I think you’ll need to swap science and philosophy around in your explanation) It’s in science that we require prediction and verification as a test of successful theory, while in philosophy only beautiful thinking would suffice

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                    1. Haelfix

                      Well perhaps philosophers should deal with quantum gravity then, b/c it’s pretty apparent that it will likely never be amenable to direct testing. Maybe if you are lucky, you might get some portion of a theories parameter space which can be indirectly probed, but that is certainly no guarantee.

                      In fact many of the ‘worst’ theories in quantum gravity, are those that spit out ‘falsifiable’ predictions. They are specifically designed with loads of cherry picked assumptions, dubious mathematical justifications and typically only address a specific problem (leaving unresolved tens of other problems that no longer have a potential solution).

                      It’s the same thing at the LHC. A lot of theories with spectacular collider signatures are theories of the worst sort. Designed, by hand, simply based upon the result and not the substance of the mathematical logic within the theory.

                      So i’d argue that the ‘falsifiability’ criterion is important, but being too dogmatic about the substance can quickly lead into all sorts of nonsense.

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  4. Giotis

    And again I say to you, It is easier for a camel to go through the eye of a needle, than for a lay man to enter into the kingdom of high energy theoretical physics and String theory.

    Mathew 19:24

    Using a theory manifesting itself at String scales to make predictions at LHC scales is like using an elephant to catch mice.

    The thing you must ask about is if such theory is able to make all the correct postdictions i.e. whether you can derive from it even in principle the low energy effective world we are inhabiting without violating mathematical and theoretical consistency within a coherent, economical self contained scheme of reduction carrying immense explanatory power.

    All these highly non trivial criteria are fulfilled by String theory epitomising in fact the very notion of a Theory of a Everything.

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