Category Archives: String Theory

Which String Theorists Are You Complaining About?

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Do string theorists have an unfair advantage? Do they have an easier time getting hired, for example?

In one of the perennial arguments about this on Twitter, Martin Bauer posted a bar chart of faculty hires in the US by sub-field. The chart was compiled by Erich Poppitz from data in the US particle physics rumor mill, a website where people post information about who gets hired where for the US’s quite small number of permanent theoretical particle physics positions at research universities and national labs. The data covers 1994 to 2017, and shows one year, 1999, when there were more string theorists hired than all other topics put together. The years around then also had many string theorists hired, but the proportion starts falling around the mid 2000’s…around when Lee Smolin wrote a book, The Trouble With Physics, arguing that string theorists had strong-armed their way into academic dominance. After that, the percentage of string theorists falls, oscillating between a tenth and a quarter of total hires.

Judging from that, you get the feeling that string theory’s critics are treating a temporary hiring fad as if it was a permanent fact. The late 1990’s were a time of high-profile developments in string theory that excited a lot of people. Later, other hiring fads dominated, often driven by experiments: I remember when the US decided to prioritize neutrino experiments and neutrino theorists had a much easier time getting hired, and there seem to be similar pushes now with gravitational waves, quantum computing, and AI.

Thinking about the situation in this way, though, ignores what many of the critics have in mind. That’s because the “string” column on that bar chart is not necessarily what people think of when they think of string theory.

If you look at the categories on Poppitz’s bar chart, you’ll notice something odd. “String” its itself a category. Another category, “lattice”, refers to lattice QCD, a method to find the dynamics of quarks numerically. The third category, though, is a combination of three things “ph/th/cosm”.

“Cosm” here refers to cosmology, another sub-field. “Ph” and “th” though aren’t really sub-fields. Instead, they’re arXiv categories, sections of the website arXiv.org where physicists post papers before they submit them to journals. The “ph” category is used for phenomenology, the type of theoretical physics where people try to propose models of the real world and make testable predictions. The “th” category is for “formal theory”, papers where theoretical physicists study the kinds of theories they use in more generality and develop new calculation methods, with insights that over time filter into “ph” work.

“String”, on the other hand, is not an arXiv category. When string theorists write papers, they’ll put them into “th” or “ph” or another relevant category (for example “gr-qc”, for general relativity and quantum cosmology). This means that when Poppitz distinguishes “ph/th/cosm” from “string”, he’s being subjective, using his own judgement to decide who counts as a string theorist.

So who counts as a string theorist? The simplest thing to do would be to check if their work uses strings. Failing that, they could use other tools of string theory and its close relatives, like Calabi-Yau manifolds, M-branes, and holography.

That might be what Poppitz was doing, but if he was, he was probably missing a lot of the people critics of string theory complain about. He even misses many people who describe themselves as string theorists. In an old post of mine I go through the talks at Strings, string theory’s big yearly conference, giving them finer-grained categories. The majority don’t use anything uniquely stringy.

Instead, I think critics of string theory have two kinds of things in mind.

First, most of the people who made their reputations on string theory are still in academia, and still widely respected. Some of them still work on string theory topics, but many now work on other things. Because they’re still widely respected, their interests have a substantial influence on the field. When one of them starts looking at connections between theories of two-dimensional materials, you get a whole afternoon of talks at Strings about theories of two-dimensional materials. Working on those topics probably makes it a bit easier to get a job, but also, many of the people working on them are students of these highly respected people, who just because of that have an easier time getting a job. If you’re a critic of string theory who thinks the founders of the field led physics astray, then you probably think they’re still leading physics astray even if they aren’t currently working on string theory.

Second, for many other people in physics, string theorists are their colleagues and friends. They’ll make fun of trends that seem overhyped and under-thought, like research on the black hole information paradox or the swampland, or hopes that a slightly tweaked version of supersymmetry will show up soon at the LHC. But they’ll happily use ideas developed in string theory when they prove handy, using supersymmetric theories to test new calculation techniques, string theory’s extra dimensions to inspire and ground new ideas for dark matter, or the math of strings themselves as interesting shortcuts to particle physics calculations. String theory is available as reference to these people in a way that other quantum gravity proposals aren’t. That’s partly due to familiarity and shared language (I remember a talk at Perimeter where string theorists wanted to learn from practitioners from another area and the discussion got bogged down by how they were using the word “dimension”), but partly due to skepticism of the various alternate approaches. Most people have some idea in their heads of deep problems with various proposals: screwing up relativity, making nonsense out of quantum mechanics, or over-interpreting on limited evidence. The most commonly believed criticisms are usually wrong, with objections long-known to practitioners of the alternate approaches, and so those people tend to think they’re being treated unfairly. But the wrong criticisms are often simplified versions of correct criticisms, passed down by the few people who dig deeply into these topics, criticisms that the alternative approaches don’t have good answers to.

The end result is that while string theory itself isn’t dominant, a sort of “string friendliness” is. Most of the jobs aren’t going to string theorists in the literal sense. But the academic world string theorists created keeps turning. People still respect string theorists and the research directions they find interesting, and people are still happy to collaborate and discuss with string theorists. For research communities people are more skeptical of, it must feel very isolating, like the world is still being run by their opponents. But this isn’t the kind of hegemony that can be solved by a revolution. Thinking that string theory is a failed research program, and people focused on it should have a harder time getting hired, is one thing. Thinking that everyone who respects at least one former string theorist should have a harder time getting hired is a very different goal. And if what you’re complaining about is “string friendliness”, not actual string theorists, then that’s what you’re asking for.

The Nowhere String

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Space and time seem as fundamental as anything can get. Philosophers like Immanuel Kant thought that they were inescapable, that we could not conceive of the world without space and time. But increasingly, physicists suspect that space and time are not as fundamental as they appear. When they try to construct a theory of quantum gravity, physicists find puzzles, paradoxes that suggest that space and time may just be approximations to a more fundamental underlying reality.

One piece of evidence that quantum gravity researchers point to are dualities. These are pairs of theories that seem to describe different situations, including with different numbers of dimensions, but that are secretly indistinguishable, connected by a “dictionary” that lets you interpret any observation in one world in terms of an equivalent observation in the other world. By itself, duality doesn’t mean that space and time aren’t fundamental: as I explained in a blog post a few years ago, it could still be that one “side” of the duality is a true description of space and time, and the other is just a mathematical illusion. To show definitively that space and time are not fundamental, you would want to find a situation where they “break down”, where you can go from a theory that has space and time to a theory that doesn’t. Ideally, you’d want a physical means of going between them: some kind of quantum field that, as it shifts, changes the world between space-time and not space-time.

What I didn’t know when I wrote that post was that physicists already knew about such a situation in 1993.

Back when I was in pre-school, famous string theorist Edward Witten was trying to understand something that others had described as a duality, and realized there was something more going on.

In string theory, particles are described by lengths of vibrating string. In practice, string theorists like to think about what it’s like to live on the string itself, seeing it vibrate. In that world, there are two dimensions, one space dimension back and forth along the string and one time dimension going into the future. To describe the vibrations of the string in that world, string theorists use the same kind of theory that people use to describe physics in our world: a quantum field theory. In string theory, you have a two-dimensional quantum field theory stuck “inside” a theory with more dimensions describing our world. You see that this world exists by seeing the kinds of vibrations your two-dimensional world can have, through a type of quantum field called a scalar field. With ten scalar fields, ten different ways you can push energy into your stringy world, you can infer that the world around you is a space-time with ten dimensions.

String theory has “extra” dimensions beyond the three of space and one of time we’re used to, and these extra dimensions can be curled up in various ways to hide them from view, often using a type of shape called a Calabi-Yau manifold. In the late 80’s and early 90’s, string theorists had found a similarity between the two-dimensional quantum field theories you get folding string theory around some of these Calabi-Yau manifolds and another type of two-dimensional quantum field theory related to theories used to describe superconductors. People called the two types of theories dual, but Witten figured out there was something more going on.

Witten described the two types of theories in the same framework, and showed that they weren’t two equivalent descriptions of the same world. Rather, they were two different ways one theory could behave.

The two behaviors were connected by something physical: the value of a quantum field called a modulus field. This field can be described by a number, and that number can be positive or negative.

When the modulus field is a large positive number, then the theory behaves like string theory twisted around a Calabi-Yau manifold. In particular, the scalar fields have many different values they can take, values that are smoothly related to each other. These values are nothing more or less than the position of the string in space and time. Because the scalars can take many values, the string can sit in many different places, and because the values are smoothly related to each other, the string can smoothly move from one place to another.

When the modulus field is a large negative number, then the theory is very different. What people thought of as the other side of the duality, a theory like the theories used to describe superconductors, is the theory that describes what happens when the modulus field is large and negative. In this theory, the scalars can no longer take many values. Instead, they have one option, one stable solution. That means that instead of there being many different places the string could sit, describing space, there are no different places, and thus no space. The string lives nowhere.

These are two very different situations, one with space and one without. And they’re connected by something physical. You could imagine manipulating the modulus field, using other fields to funnel energy into it, pushing it back and forth from a world with space to a world of nowhere. Much more than the examples I was aware of, this is a super-clear example of a model where space is not fundamental, but where it can be manipulated, existing or not existing based on physical changes.

We don’t know whether a model like this describes the real world. But it’s gratifying to know that it can be written down, that there is a picture, in full mathematical detail, of how this kind of thing works. Hopefully, it makes the idea that space and time are not fundamental sound a bit more reasonable.

The Multiverse You Can Visit Is Not the True Multiverse

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I don’t want to be the kind of science blogger who constantly complains about science fiction, but sometimes I can’t help myself.

When I blogged about zero-point energy a few weeks back, there was a particular book that set me off. Ian McDonald’s River of Gods depicts the interactions of human and AI agents in a fragmented 2047 India. One subplot deals with a power company pursuing zero-point energy, using an imagined completion of M theory called M* theory. This post contains spoilers for that subplot.

What frustrated me about River of Gods is that the physics in it almost makes sense. It isn’t just an excuse for magic, or a standard set of tropes. Even the name “M* theory” is extremely plausible, the sort of term that could get used for technical reasons in a few papers and get accidentally stuck as the name of our fundamental theory of nature. But because so much of the presentation makes sense, it’s actively frustrating when it doesn’t.

The problem is the role the landscape of M* theory plays in the story. The string theory (or M theory) landscape is the space of all consistent vacua, a list of every consistent “default” state the world could have. In the story, one of the AIs is trying to make a portal to somewhere else in the landscape, a world of pure code where AIs can live in peace without competing with humans.

The problem is that the landscape is not actually a real place in string theory. It’s a metaphorical mathematical space, a list organized by some handy coordinates. The other vacua, the other “default states”, aren’t places you can travel to, there just other ways the world could have been.

Ok, but what about the multiverse?

There are physicists out there who like to talk about multiple worlds. Some think they’re hypothetical, others argue they must exist. Sometimes they’ll talk about the string theory landscape. But to get a multiverse out of the string theory landscape, you need something else as well.

Two options for that “something else” exist. One is called eternal inflation, the other is the many-worlds interpretation of quantum mechanics. And neither lets you travel around the multiverse.

In eternal inflation, the universe is expanding faster and faster. It’s expanding so fast that, in most places, there isn’t enough time for anything complicated to form. Occasionally, though, due to quantum randomness, a small part of the universe expands a bit more slowly: slow enough for stars, planets, and maybe life. Each small part like that is its own little “Big Bang”, potentially with a different “default” state, a different vacuum from the string landscape. If eternal inflation is true then you can get multiple worlds, but they’re very far apart, and getting farther every second: not easy to visit.

The many-worlds interpretation is a way to think about quantum mechanics. One way to think about quantum mechanics is to say that quantum states are undetermined until you measure them: a particle could be spinning left or right, Schrödinger’s cat could be alive or dead, and only when measured is their state certain. The many-worlds interpretation offers a different way: by doing away with measurement, it instead keeps the universe in the initial “undetermined” state. The universe only looks determined to us because of our place in it: our states become entangled with those of particles and cats, so that our experiences only correspond to one determined outcome, the “cat alive branch” or the “cat dead branch”. Combine this with the string landscape, and our universe might have split into different “branches” for each possible stable state, each possible vacuum. But you can’t travel to those places, your experiences are still “just on one branch”. If they weren’t, many-worlds wouldn’t be an interpretation, it would just be obviously wrong.

In River of Gods, the AI manipulates a power company into using a particle accelerator to make a bubble of a different vacuum in the landscape. Surprisingly, that isn’t impossible. Making a bubble like that is a bit like what the Large Hadron Collider does, but on a much larger scale. When the Large Hadron Collider detected a Higgs boson, it had created a small ripple in the Higgs field, a small deviation from its default state. One could imagine a bigger ripple doing more: with vastly more energy, maybe you could force the Higgs all the way to a different default, a new vacuum in its landscape of possibilities.

Doing that doesn’t create a portal to another world, though. It destroys our world.

That bubble of a different vacuum isn’t another branch of quantum many-worlds, and it isn’t a far-off big bang from eternal inflation. It’s a part of our own universe, one with a different “default state” where the particles we’re made of can’t exist. And typically, a bubble like that spreads at the speed of light.

In the story, they have a way to stabilize the bubble, stop it from growing or shrinking. That’s at least vaguely believable. But it means that their “portal to another world” is just a little bubble in the middle of a big expensive device. Maybe the AI can live there happily…until the humans pull the plug.

Or maybe they can’t stabilize it, and the bubble spreads and spreads at the speed of light destroying everything. That would certainly be another way for the AI to live without human interference. It’s a bit less peaceful than advertised, though.

Hadronic Strings and Large-N Field Theory at NBI

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One of string theory’s early pioneers, Michael Green, is currently visiting the Niels Bohr Institute as part of a program by the Simons Foundation. The program includes a series of conferences. This week we are having the first such conference, on Hadronic Strings and Large-N Field Theory.

The bulk of the conference focused on new progress on an old subject, using string theory to model the behavior of quarks and gluons. There were a variety of approaches on offer, some focused on particular approximations and others attempting to construct broader, “phenomenological” models.

The other talks came from a variety of subjects, loosely tied together by the topic of “large N field theories”. “N” here is the number of colors: while the real world has three “colors” of quarks, you can imagine a world with more. This leads to simpler calculations, and often to connections with string theory. Some talks deal with attempts to “solve” certain large-N theories exactly. Others ranged farther afield, even to discussions of colliding black holes.

How to Get a “Minimum Scale” Without Pixels

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Zoom in, and the world gets stranger. Down past atoms, past protons and neutrons, far past the smallest scales we can probe at the Large Hadron Collider, we get to the scale at which quantum gravity matters: the Planck scale.

Weird things happen at the Planck scale. Space and time stop making sense. Read certain pop science articles, and they’ll tell you the Planck scale is the smallest scale, the scale where space and time are quantized, the “pixels of the universe”.

That last sentence, by the way, is not actually how the Planck scale works. In fact, there’s pretty good evidence that the universe doesn’t have “pixels”, that space and time are not quantized in that way. Even very tiny pixels would change the speed of light, making it different for different colors. Tiny effects like that add up, and astronomers would almost certainly have noticed an effect from even Planck-scale pixels. Unless your idea of “pixels” is fairly unusual, it’s already been ruled out.

If the Planck scale isn’t the scale of the “pixels of the universe”, why do people keep saying it is?

Part of the problem is that the real story is vaguer. We don’t know what happens at the Planck scale. It’s not just that we don’t know which theory of quantum gravity is right: we don’t even know what different quantum gravity proposals predict. People are trying to figure it out, and there are some more or less viable ideas, but ultimately all we know is that at the Planck scale our description of space-time should break down.

“Our description breaks down” is unfortunately not very catchy. Certainly, it’s less catchy than “pixels of the universe”. Part of the problem is that most people don’t know what “our description breaks down” actually means.

So if that’s the part that’s puzzling you, maybe an example would help. This won’t be the full answer, though it could be part of the story. What it will be is an example of what “our description breaks down” can actually mean, how there can be a scale beyond which space-time stops making sense without there being “pixels”.

The example comes from string theory, from a concept called “T duality”. In string theory, “extra” dimensions beyond our usual three space and one time are curled up small, so that traveling along them just gets you back where you started. Instead of particles, there are strings, with length close to the Planck length.

Picture a loop of string in a small extra dimension. What can it do?

Image credit: someone who’s done a lot more work explaining string theory than I have

One thing it can do is move along the extra dimension. Since it has to end up back where it started, it can’t just move at any speed it wants. It turns out that the smaller the extra dimension, the more energy the string has when it spins around it.

The other thing it can do is wrap around the extra dimension. If it wraps around, the string has more energy if the dimension is larger, like a rubber band stretched around a pipe.

The string can do either or both of these multiple times. It can wrap many times around the extra dimension, or move in a quicker circle around it, or both at once. And if you calculate the energy of these combinations, you notice something: a string wound around a big circle has the same energy as a string moving around a small circle. In particular, you get the same energy on a circle of radius R, and a circle of radius l^2/R, where l is the length of the string.

It turns out it’s not just the energy that’s the same: for everything that happens on a circle of radius R, there’s a matching description with a circle of radius l^2/R, with wrapping and moving swapped. We say that the two descriptions are dual: two seemingly different pictures that turn out to be completely physically indistinguishable.

Since the two pictures are indistinguishable, it doesn’t actually make sense to talk about dimensions smaller than the length of the string. It’s not that they can’t exist, or that they’re smaller than the “pixels of the universe”: it’s just that any description you write down of such a small dimension could just as easily have been of a larger, dual dimension. It’s that your picture, of one obvious size of the curled up dimension, broke down and stopped making sense.

As I mentioned, this isn’t the whole picture of what happens at the Planck scale, even in string theory. It is an example of a broader idea that string theorists are investigating, that in order to understand space-time at the smallest scales you need to understand many different dual descriptions. And hopefully, it’s something you can hold in your mind, a specific example of what “our description breaks down” can actually mean in practice, without pixels.

Strings 2018

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I’m at Strings this week, in tropical Okinawa. Opening the conference, organizer Hirosi Ooguri joked that they had carefully scheduled things for a sunny time of year, and since the rainy season had just ended “who says that string theorists don’t make predictions?”

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There was then a rainstorm during lunch, falsifying string theory

This is the first time I’ve been to Strings. There are almost 500 people here, which might seem small for folks in other fields, but for me this is the biggest conference I’ve attended. The size is noticeable in the little things: this is the first conference I’ve been to with a diaper changing room, the first managed by a tour company, the first with a dedicated “Cultural Evening” featuring classical music from the region. With this in mind, the conference were impressively well-organized, but there were some substantial gaps (tightly packed tours before the Cultural Evening that didn’t leave time for dinner, and a talk by Morrison cut short by missing slides that offset the schedule of the whole last day).

On the well-organized side, Strings has a particular structure for its talks, with Review Talks and Plenary Talks. The Review Talks each summarize a subject: mostly main focuses of the conference, but with a few (Ashoke Sen on String Field Theory, David Simmons-Duffin on the Conformal Bootstrap) that only covered the content of a few talks.

I’m not going to make another pie chart this year, if you want that kind of breakdown Daniel Harlow gave one during the “Golden Jubilee” at the end. If I did something like that this time, I’d divide it up not by sub-fields, but by goals. Talks here focused on a few big questions: “Can we classify all quantum field theories?” “What are the general principles behind quantum gravity?” “Can we make some of the murky aspects of string theory clearer?” “How can string theory give rise to sensible physics in four dimensions?”

Of those questions, classifying quantum field theories made up the bulk of the conference. I’ve heard people dismiss this work on the ground that much of it only works in supersymmetric theories. With that in mind, it was remarkable just how much of the conference was non-supersymmetric. Supersymmetry still played a role, but the assumption seemed to be that it was more of a sub-topic than something universal (to the extent that one of the Review Talks, Clay Cordova’s “What’s new with Q?”, was “the supersymmetry review talk”). Both supersymmetric and non-supersymmetric theories are increasingly understood as being part of a “landscape”, linked by duality and thinking at different scales. These links are sometimes understood in terms of string theory, but often not. So far it’s not clear if there is a real organizing principle here, especially for the non-supersymmetric cases, and people seem to be kept busy enough just proving the links they observe.

Finding general principles behind quantum gravity motivated a decent range of the talks, from Andrew Strominger to Jorge Santos. The topics that got the most focus, and two of the Review Talks, were by what I’ve referred to as “entanglers”, people investigating the structure of space and time via quantum entanglement and entropy. My main takeaway from these talks was perhaps a bit frivolous: between Maldacena’s talk (about an extremely small wormhole made from Standard Model-compatible building blocks) and Hartman’s discussion of the Average Null Energy Condition, it looks like a “useful sci-fi wormhole” (specifically, one that gets you there faster than going the normal way) has been conclusively ruled out in quantum field theory.

Only a minority of talks discussed using string theory to describe the real world, though I get the impression this was still more focus than in past years. In particular, there were several talks trying to discover properties of Calabi-Yaus, the geometries used to curl up string theory’s extra dimensions. Watching these talks I had a similar worry to Strominger’s question after Irene Valenzuela’s talk: it’s not clear that these investigations aren’t just examining a small range of possibilities, one that might become irrelevant if new dualities or types of compactification are found. Ironically, this objection seems to apply least to Valenzuela’s talk itself: characterizing the “swampland” of theories that don’t make sense as part of a theory of quantum gravity may start with examples from string compactifications, but its practitioners are looking for more general principles about quantum gravity and seem to manage at least reasonable arguments that don’t depend on string theory being true.

There wasn’t much from the amplitudes field at this conference, with just Yu-tin Huang’s talk carrying that particular flag. Despite that, amplitudes methods came up in several talks, with Silviu Pufu praising an amplitudes textbook and David Simmons-Duffin bringing up amplitudes several times (more than he did in his talk last week at Amplitudes).

The end of the conference featured a panel discussion in honor of String Theory’s 50th Anniversary, its “Golden Jubilee”. The panel was evenly split between founders of string theory, heroes of the string duality revolution, and the current crop of young theorists. The panelists started by each giving a short presentation. Michael Green joked that it felt like a “geriatric gong show”, and indeed a few of the presentations were gong show-esque. Still, some of the speeches were inspiring. I was particularly impressed by Juan Maldacena, Eva Silverstein, and Daniel Harlow, who each laid out a compelling direction for string theory’s future. The questions afterwards were collated by David Gross from audience submissions, and were largely what you would expect, with quite a lot of questions about whether string theory can ever connect with experiment. I was more than a little disappointed by the discussion of whether string theory can give rise to de Sitter space, which was rather botched: Maldacena was appointed as the defender of de Sitter, but (contra Gross’s summary) the quantum complexity-based derivation he proposed didn’t sound much like the flux compactifications that have inspired so much controversy, so everyone involved ended up talking past each other.

Edit: See Shamit’s comment below, I apparently misunderstood what Maldacena was referring to.

Epistemology, Not Metaphysics, Justifies Experiments

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While I was visiting the IAS a few weeks back, they had a workshop on Quantum Information and Black Holes. I didn’t see many of the talks, but I did get to see Leonard Susskind talk about his new slogan, GR=QM.

For some time now, researchers have been uncovering deep connections between gravity and quantum mechanics. Juan Maldacena jump-started the field with the discovery of AdS/CFT, showing that theories that describe gravity in a particular curved space (Anti-de Sitter, or AdS) are equivalent to non-gravity quantum theories describing the boundary of that space (specifically, Conformal Field Theories, or CFTs). The two theories contain the same information and, with the right “dictionary”, describe the same physics: in our field’s vernacular, they’re dual. Since then, physicists have found broader similarities, situations where properties of quantum mechanics, like entanglement, are closely linked to properties of gravity theories. Maldacena’s ER=EPR may be the most publicized of these, a conjectured equivalence between Einstein-Rosen bridges (colloquially known as wormholes) and entangled pairs of particles (famously characterized by Einstein, Podolsky, and Rosen).

GR=QM is clearly a riff on ER=EPR, but Susskind is making a more radical claim. Based on these developments, including his own work on quantum complexity, Susskind is arguing that the right kind of quantum mechanical system automatically gives rise to quantum gravity. What’s more, he claims that these systems will be available, using quantum computers, within roughly a decade. Within ten years or so, we’ll be able to do quantum gravity experiments.

That sounds ridiculous, until you realize he’s talking about dual theories. What he’s imagining is not an experiment at the absurdly high energies necessary to test quantum gravity, but rather a low-energy quantum mechanics experiment that is equivalent, by something like AdS/CFT, to a quantum gravity experiment.

Most people would think of that as a simulation, not an actual test of quantum gravity. Susskind, though, spends quite a bit of time defending the claim that it really is gravity, that literally GR=QM. His description of clever experiments and overarching physical principles is aimed at piling on evidence for that particular claim.

What do I think? I don’t think it matters much.

The claim Susskind is making is one of metaphysics: the philosophy of which things do and do not “really” exist. Unlike many physicists, I think metaphysics is worth discussing, that there are philosophers who make real progress with it.

But ultimately, Susskind is proposing a set of experiments. And what justifies experiments isn’t metaphysics, it’s epistemology: not what’s “really there”, but what we can learn.

What can we learn from the sorts of experiments Susskind is proposing?

Let’s get this out of the way first: we can’t learn which theory describes quantum gravity in our own world.

That’s because every one of these experiments relies on setting up a quantum system with particular properties. Every time, you’re choosing the “boundary theory”, the quantum mechanical side of GR=QM. Either you choose a theory with a known gravity partner, and you know how the inside should behave, or you choose a theory with an unknown partner. Either way, you have no reason to expect the gravity side to resemble the world we live in.

Plenty of people would get suspicious of Susskind here, and accuse him of trying to mislead people. They’re imagining headlines, “Experiment Proves String Theory”, based on a system intentionally set up to have a string theory dual, a system that can’t actually tell us whether string theory describes the real world.

That’s not where I’m going with this.

The experiments that Susskind is describing can’t prove string theory. But we could still learn something from them.

For one, we could learn whether these pairs of theories really are equivalent. AdS/CFT, ER=EPR, these are conjectures. In some cases, they’re conjectures with very good evidence. But they haven’t been proven, so it’s still possible there’s a problem people overlooked. One of the nice things about experiments and simulations is that they’re very good at exposing problems that were overlooked.

For another, we could get a better idea of how gravity behaves in general. By simulating a wide range of theories, we could look for overarching traits, properties that are common to most gravitational theories. We wouldn’t be sure that those properties hold in our world…but with enough examples, we could get pretty confident. Hopefully, we’d stumble on things that gravity has to do, in order to be gravity.

Susskind is quite capable of making these kinds of arguments, vastly more so than I. So it frustrates me that every time I’ve seen him talk or write about this, he hasn’t. Instead, he keeps framing things in terms of metaphysics, whether quantum mechanics “really is” gravity, whether the experiment “really” explores a wormhole. If he wants to usher in a new age of quantum gravity experiments, not just as a buzzword but as real, useful research, then eventually he’s going to have to stop harping on metaphysics and start talking epistemology. I look forward to when that happens.

Thoughts on Polchinski’s Memoir

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I didn’t get a chance to meet Joseph Polchinski when I was visiting Santa Barbara last spring. At the time, I heard his health was a bit better, but he still wasn’t feeling well enough to come in to campus. Now that I’ve read his memoir, I almost feel like I have met him. There’s a sense of humor, a diffidence, and a passion for physics that shines through the pages.

The following are some scattered thoughts inspired by the memoir:

 

A friend of mine once complained to me that in her field grad students all brag about the colleges they went to. I mentioned that in my field your undergrad never comes up…unless it was Caltech. For some reason, everyone I’ve met who went to Caltech is full of stories about the place, and Polchinski is no exception. Speaking as someone who didn’t go there, it seems like Caltech has a profound effect on its students that other places don’t.

 

Polchinski mentions hearing stories about geniuses of the past, and how those stories helped temper some of his youthful arrogance. There’s an opposite effect that’s also valuable: hearing stories like Polchinski’s, his descriptions of struggling with anxiety and barely publishing and “not really accomplishing anything” till age 40, can be a major comfort to those of us who worry we’ve fallen behind in the academic race. That said, it’s important not to take these things too far: times have changed, you’re not Polchinski, and much like his door-stealing trick at Caltech getting a postdoc without any publications is something you shouldn’t try at home. Even Witten’s students need at least one.

 

Last week I was a bit puzzled by nueww’s comment, a quote from Polchinski’s memoir which distinguishes “math of the equations” from “math of the solutions”, attributing the former to physicists and the latter to mathematicians. Reading the context in the memoir and the phrase’s origin in a remark by Susskind cleared up a bit, but still left me uneasy. I only figured out why after Lubos Motl posted about it: it doesn’t match my experience of mathematicians at all!

If anything, I think physicists usually care more about the “solutions” than mathematicians do. In my field, often a mathematician will construct some handy basis of functions and then frustrate everyone by providing no examples of how to use them. In the wider math community I’ve met graph theorists who are happy to prove something is true for all graphs of size 10^{10^10} and larger, not worrying about the vast number of graphs where it fails because it’s just a finite number of special cases. And I don’t think this is just my experience: a common genre of jokes revolve around mathematicians proving a solution exists and then not bothering to do anything with it (for example, see the joke with the hotel fire here).

I do think there’s a meaningful sense in which mathematicians care about details that we’re happy to ignore, but “solutions” versus “equations” isn’t really the right axis. It’s something more like “rigor” versus “principles”. Mathematicians will often begin a talk by defining a series of maps between different spaces, carefully describing where they are and aren’t valid. A physicist might just write down a function. That sort of thing is dangerous in mathematics: there are always special, pathological cases that make careful definitions necessary. In physics, those cases rarely come up, and when they do there’s often a clear physical problem that brings them to the forefront. We have a pretty good sense of when we need rigor, and when we don’t we’re happy to lay things out without filling in the details, putting a higher priority on moving forward and figuring out the basic principles underlying reality.

 

Polchinski talks a fair bit about his role in the idea of the multiverse, from hearing about Weinberg’s anthropic argument to coming to terms with the string landscape. One thing his account makes clear is how horrifying the concept seemed at first: how the idea that the parameters of our universe might just be random could kill science and discourage experimentalists. This touches on something that I think gets lost in arguments about the multiverse: even the people most involved in promoting the multiverse in public aren’t happy about it.

It also sharpened my thinking about the multiverse a bit. I’ve talked before about how I don’t think the popularity of the multiverse is actually going to hurt theoretical physics as a field. Polchinski’s worries made me think about the experimental side of the equation: why do experiments if the world might just be random? I think I have a clearer answer to this now, but it’s a bit long, so I’ll save it for a future post.

 

One nice thing about these long-term accounts is you get to see how much people shift between fields over time. Polchinski didn’t start out working in string theory, and most of the big names in my field, like Lance Dixon and David Kosower, didn’t start out in scattering amplitudes. Academic careers are long, and however specialized we feel at any one time we can still get swept off in a new direction.

 

I’m grateful for this opportunity to “meet” Polchinski, if only through his writing. His is a window on the world of theoretical physics that is all too rare, and valuable as a result.

The Way You Think Everything Is Connected Isn’t the Way Everything Is Connected

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I hear it from older people, mostly.

“Oh, I know about quantum physics, it’s about how everything is connected!”

“String theory: that’s the one that says everything is connected, right?”

“Carl Sagan said we are all stardust. So really, everything is connected.”

connect_four

It makes Connect Four a lot easier anyway

I always cringe a little when I hear this. There’s a misunderstanding here, but it’s not a nice clean one I can clear up in a few sentences. It’s a bunch of interconnected misunderstandings, mixing some real science with a lot of confusion.

To get it out of the way first, no, string theory is not about how “everything is connected”. String theory describes the world in terms of strings, yes, but don’t picture those strings as links connecting distant places: string theory’s proposed strings are very, very short, much smaller than the scales we can investigate with today’s experiments. The reason they’re thought to be strings isn’t because they connect distant things, it’s because it lets them wiggle (counteracting some troublesome wiggles in quantum gravity) and wind (curling up in six extra dimensions in a multitude of ways, giving us what looks like a lot of different particles).

(Also, for technical readers: yes, strings also connect branes, but that’s not the sort of connection these people are talking about.)

What about quantum mechanics?

Here’s where it gets trickier. In quantum mechanics, there’s a phenomenon called entanglement. Entanglement really does connect things in different places…for a very specific definition of “connect”. And there’s a real (but complicated) sense in which these connections end up connecting everything, which you can read about here. There’s even speculation that these sorts of “connections” in some sense give rise to space and time.

You really have to be careful here, though. These are connections of a very specific sort. Specifically, they’re the sort that you can’t do anything through.

Connect two cans with a length of string, and you can send messages between them. Connect two particles with entanglement, though, and you can’t send messages between them…at least not any faster than between two non-entangled particles. Even in a quantum world, physics still respects locality: the principle that you can only affect the world where you are, and that any changes you make can’t travel faster than the speed of light. Ansibles, science-fiction devices that communicate faster than light, can’t actually exist according to our current knowledge.

What kind of connection is entanglement, then? That’s a bit tricky to describe in a short post. One way to think about entanglement is as a connection of logic.

Imagine someone takes a coin and cuts it along the rim into a heads half and a tails half. They put the two halves in two envelopes, and randomly give you one. You don’t know whether you have heads or tails…but you know that if you open your envelope and it shows heads, the other envelope must have tails.

m_nickel

Unless they’re a spy. Then it could contain something else.

Entanglement starts out with connections like that. Instead of a coin, take a particle that isn’t spinning and “split” it into two particles spinning in different directions, “spin up” and “spin down”. Like the coin, the two particles are “logically connected”: you know if one of them is “spin up” the other is “spin down”.

What makes a quantum coin different from a classical coin is that there’s no way to figure out the result in advance. If you watch carefully, you can see which coin gets put in to which envelope, but no matter how carefully you look you can’t predict which particle will be spin up and which will be spin down. There’s no “hidden information” in the quantum case, nowhere nearby you can look to figure it out.

That makes the connection seem a lot weirder than a regular logical connection. It also has slightly different implications, weirdness in how it interacts with the rest of quantum mechanics, things you can exploit in various ways. But none of those ways, none of those connections, allow you to change the world faster than the speed of light. In a way, they’re connecting things in the same sense that “we are all stardust” is connecting things: tied together by logic and cause.

So as long as this is all you mean by “everything is connected” then sure, everything is connected. But often, people seem to mean something else.

Sometimes, they mean something explicitly mystical. They’re people who believe in dowsing rods and astrology, in sympathetic magic, rituals you can do in one place to affect another. There is no support for any of this in physics. Nothing in quantum mechanics, in string theory, or in big bang cosmology has any support for altering the world with the power of your mind alone, or the stars influencing your day to day life. That’s just not the sort of connection we’re talking about.

Sometimes, “everything is connected” means something a bit more loose, the idea that someone’s desires guide their fate, that you could “know” something happened to your kids the instant it happens from miles away. This has the same problem, though, in that it’s imagining connections that let you act faster than light, where people play a special role. And once again, these just aren’t that sort of connection.

Sometimes, finally, it’s entirely poetic. “Everything is connected” might just mean a sense of awe at the deep physics in mundane matter, or a feeling that everyone in the world should get along. That’s fine: if you find inspiration in physics then I’m glad it brings you happiness. But poetry is personal, so don’t expect others to find the same inspiration. Your “everyone is connected” might not be someone else’s.

The Parable of the Entanglers and the Bootstrappers

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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.