Tag Archives: string theory

How Small Scales Can Matter for Large Scales

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For a certain type of physicist, nothing matters more than finding the ultimate laws of nature for its tiniest building-blocks, the rules that govern quantum gravity and tell us where the other laws of physics come from. But because they know very little about those laws at this point, they can predict almost nothing about observations on the larger distance scales we can actually measure.

“Almost nothing” isn’t nothing, though. Theoretical physicists don’t know nature’s ultimate laws. But some things about them can be reasonably guessed. The ultimate laws should include a theory of quantum gravity. They should explain at least some of what we see in particle physics now, explaining why different particles have different masses in terms of a simpler theory. And they should “make sense”, respecting cause and effect, the laws of probability, and Einstein’s overall picture of space and time.

All of these are assumptions, of course. Further assumptions are needed to derive any testable consequences from them. But a few communities in theoretical physics are willing to take the plunge, and see what consequences their assumptions have.

First, there’s the Swampland. String theorists posit that the world has extra dimensions, which can be curled up in a variety of ways to hide from view, with different observable consequences depending on how the dimensions are curled up. This list of different observable consequences is referred to as the Landscape of possibilities. Based on that, some string theorists coined the term “Swampland” to represent an area outside the Landscape, containing observations that are incompatible with quantum gravity altogether, and tried to figure out what those observations would be.

In principle, the Swampland includes the work of all the other communities on this list, since a theory of quantum gravity ought to be consistent with other principles as well. In practice, people who use the term focus on consequences of gravity in particular. The earliest such ideas argued from thought experiments with black holes, finding results that seemed to demand that gravity be the weakest force for at least one type of particle. Later researchers would more frequently use string theory as an example, looking at what kinds of constructions people had been able to make in the Landscape to guess what might lie outside of it. They’ve used this to argue that dark energy might be temporary, and to try to figure out what traits new particles might have.

Second, I should mention naturalness. When talking about naturalness, people often use the analogy of a pen balanced on its tip. While possible in principle, it must have been set up almost perfectly, since any small imbalance would cause it to topple, and that perfection demands an explanation. Similarly, in particle physics, things like the mass of the Higgs boson and the strength of dark energy seem to be carefully balanced, so that a small change in how they were set up would lead to a much heavier Higgs boson or much stronger dark energy. The need for an explanation for the Higgs’ careful balance is why many physicists expected the Large Hadron Collider to discover additional new particles.

As I’ve argued before, this kind of argument rests on assumptions about the fundamental laws of physics. It assumes that the fundamental laws explain the mass of the Higgs, not merely by giving it an arbitrary number but by showing how that number comes from a non-arbitrary physical process. It also assumes that we understand well how physical processes like that work, and what kinds of numbers they can give. That’s why I think of naturalness as a type of argument, much like the Swampland, that uses the smallest scales to constrain larger ones.

Third is a host of constraints that usually go together: causality, unitarity, and positivity. Causality comes from cause and effect in a relativistic universe. Because two distant events can appear to happen in different orders depending on how fast you’re going, any way to send signals faster than light is also a way to send signals back in time, causing all of the paradoxes familiar from science fiction. Unitarity comes from quantum mechanics. If quantum calculations are supposed to give the probability of things happening, those probabilities should make sense as probabilities: for example, they should never go above one.

You might guess that almost any theory would satisfy these constraints. But if you extend a theory to the smallest scales, some theories that otherwise seem sensible end up failing this test. Actually linking things up takes other conjectures about the mathematical form theories can have, conjectures that seem more solid than the ones underlying Swampland and naturalness constraints but that still can’t be conclusively proven. If you trust the conjectures, you can derive restrictions, often called positivity constraints when they demand that some set of observations is positive. There has been a renaissance in this kind of research over the last few years, including arguments that certain speculative theories of gravity can’t actually work.

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.

I Ain’t Afraid of No-Ghost Theorems

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In honor of Halloween this week, let me say a bit about the spookiest term in physics: ghosts.

In particle physics, we talk about the universe in terms of quantum fields. There is an electron field for electrons, a gluon field for gluons, a Higgs field for Higgs bosons. The simplest fields, for the simplest particles, can be described in terms of just a single number at each point in space and time, a value describing how strong the field is. More complicated fields require more numbers.

Most of the fundamental forces have what we call vector fields. They’re called this because they are often described with vectors, lists of numbers that identify a direction in space and time. But these vectors actually contain too many numbers.

These extra numbers have to be tidied up in some way in order to describe vector fields in the real world, like the electromagnetic field or the gluon field of the strong nuclear force. There are a number of tricks, but the nicest is usually to add some extra particles called ghosts. Ghosts are designed to cancel out the extra numbers in a vector, leaving the right description for a vector field. They’re set up mathematically such that they can never be observed, they’re just a mathematical trick.

Mathematical tricks aren’t all that spooky (unless you’re scared of mathematics itself, anyway). But in physics, ghosts can take on a spookier role as well.

In order to do their job cancelling those numbers, ghosts need to function as a kind of opposite to a normal particle, a sort of undead particle. Normal particles have kinetic energy: as they go faster and faster, they have more and more energy. Said another way, it takes more and more energy to make them go faster. Ghosts have negative kinetic energy: the faster they go, the less energy they have.

If ghosts are just a mathematical trick, that’s fine, they’ll do their job and cancel out what they’re supposed to. But sometimes, physicists accidentally write down a theory where the ghosts aren’t just a trick cancelling something out, but real particles you could detect, without anything to hide them away.

In a theory where ghosts really exist, the universe stops making sense. The universe defaults to the lowest energy it can reach. If making a ghost particle go faster reduces its energy, then the universe will make ghost particles go faster and faster, and make more and more ghost particles, until everything is jam-packed with super-speedy ghosts unto infinity, never-ending because it’s always possible to reduce the energy by adding more ghosts.

The absence of ghosts, then, is a requirement for a sensible theory. People prove theorems showing that their new ideas don’t create ghosts. And if your theory does start seeing ghosts…well, that’s the spookiest omen of all: an omen that your theory is wrong.

Why Quantum Gravity Is Controversial

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Merging quantum mechanics and gravity is a famously hard physics problem. Explaining why merging quantum mechanics and gravity is hard is, in turn, a very hard science communication problem. The more popular descriptions tend to lead to misunderstandings, and I’ve posted many times over the years to chip away at those misunderstandings.

Merging quantum mechanics and gravity is hard…but despite that, there are proposed solutions. String Theory is supposed to be a theory of quantum gravity. Loop Quantum Gravity is supposed to be a theory of quantum gravity. Asymptotic Safety is supposed to be a theory of quantum gravity.

One of the great virtues of science and math is that we are, eventually, supposed to agree. Philosophers and theologians might argue to the end of time, but in math we can write down a proof, and in science we can do an experiment. If we don’t yet have the proof or the experiment, then we should reserve judgement. Either way, there’s no reason to get into an unproductive argument.

Despite that, string theorists and loop quantum gravity theorists and asymptotic safety theorists, famously, like to argue! There have been bitter, vicious, public arguments about the merits of these different theories, and decades of research doesn’t seem to have resolved them. To an outside observer, this makes quantum gravity seem much more like philosophy or theology than like science or math.

Why is there still controversy in quantum gravity? We can’t do quantum gravity experiments, sure, but if that were the problem physicists could just write down the possibilities and leave it at that. Why argue?

Some of the arguments are for silly aesthetic reasons, or motivated by academic politics. Some are arguments about which approaches are likely to succeed in future, which as always is something we can’t actually reliably judge. But the more justified arguments, the strongest and most durable ones, are about a technical challenge. They’re about something called non-perturbative physics.

Most of the time, when physicists use a theory, they’re working with an approximation. Instead of the full theory, they’re making an assumption that makes the theory easier to use. For example, if you assume that the velocity of an object is small, you can use Newtonian physics instead of special relativity. Often, physicists can systematically relax these assumptions, including more and more of the behavior of the full theory and getting a better and better approximation to the truth. This process is called perturbation theory.

Other times, this doesn’t work well. The full theory has some trait that isn’t captured by the approximations, something that hides away from these systematic tools. The theory has some important aspect that is non-perturbative.

Every proposed quantum gravity theory uses approximations like this. The theory’s proponents try to avoid these approximations when they can, but often they have to approximate and hope they don’t miss too much. The opponents, in turn, argue that the theory’s proponents are missing something important, some non-perturbative fact that would doom the theory altogether.

Asymptotic Safety is built on top of an approximation, one different from what other quantum gravity theorists typically use. To its proponents, work using their approximation suggests that gravity works without any special modifications, that the theory of quantum gravity is easier to find than it seems. Its opponents aren’t convinced, and think that the approximation is missing something important which shows that gravity needs to be modified.

In Loop Quantum Gravity, the critics think their approximation misses space-time itself. Proponents of Loop Quantum Gravity have been unable to prove that their theory, if you take all the non-perturbative corrections into account, doesn’t just roll up all of space and time into a tiny spiky ball. They expect that their theory should allow for a smooth space-time like we experience, but the critics aren’t convinced, and without being able to calculate the non-perturbative physics neither side can convince the other.

String Theory was founded and originally motivated by perturbative approximations. Later, String Theorists figured out how to calculate some things non-perturbatively, often using other simplifications like supersymmetry. But core questions, like whether or not the theory allows a positive cosmological constant, seem to depend on non-perturbative calculations that the theory gives no instructions for how to do. Some critics don’t think there is a consistent non-perturbative theory at all, that the approximations String Theorists use don’t actually approximate to anything. Even within String Theory, there are worries that the theory might try to resist approximation in odd ways, becoming more complicated whenever a parameter is small enough that you could use it to approximate something.

All of this would be less of a problem with real-world evidence. Many fields of science are happy to use approximations that aren’t completely rigorous, as long as those approximations have a good track record in the real world. In general though, we don’t expect evidence relevant to quantum gravity any time soon. Maybe we’ll get lucky, and studies of cosmology will reveal something, or an experiment on Earth will have a particularly strange result. But nature has no obligation to help us out.

Without evidence, though, we can still make mathematical progress. You could imagine someone proving that the various perturbative approaches to String Theory become inconsistent when stitched together into a full non-perturbative theory. Alternatively, you could imagine someone proving that a theory like String Theory is unique, that no other theory can do some key thing that it does. Either of these seems unlikely to come any time soon, and most researchers in these fields aren’t pursuing questions like that. But the fact the debate could be resolved means that it isn’t just about philosophy or theology. There’s a real scientific, mathematical controversy, one rooted in our inability to understand these theories beyond the perturbative methods their proponents use. And while I don’t expect it to be resolved any time soon, one can always hold out hope for a surprise.

Amplitudes 2024, Continued

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I’ve now had time to look over the rest of the slides from the Amplitudes 2024 conference, so I can say something about Thursday and Friday’s talks.

Thursday was gravity-focused. Zvi Bern’s review talk was actually a review, a tour of the state of the art in using amplitudes techniques to make predictions for gravitational wave physics. Bern emphasized that future experiments will require much more precision: two more orders of magnitude, which in our lingo amounts to two more “loops”. The current state of the art is three loops, but they’ve been hacking away at four, doing things piece by piece in a way that cleverly also yields publications (for example, they can do just the integrals needed for supergravity, which are simpler). Four loops here is the first time that the Feynman diagrams involve Calabi-Yau manifolds, so they will likely need techniques from some of the folks I talked about last week. Once they have four loops, they’ll want to go to five, since that is the level of precision you need to learn something about the material in neutron stars. The talk covered a variety of other developments, some of which were talked about later on Thursday and some of which were only mentioned here.

Of that day’s other speakers, Stefano De Angelis, Lucile Cangemi, Mikhail Ivanov, and Alessandra Buonanno also focused on gravitational waves. De Angelis talked about the subtleties that show up when you try to calculate gravitational waveforms directly with amplitudes methods, showcasing various improvements to the pipeline there. Cangemi talked about a recurring question with its own list of subtleties, namely how the Kerr metric for spinning black holes emerges from the math of amplitudes of spinning particles. Gravitational waves were the focus of only the second half of Ivanov’s talk, where he talked about how amplitudes methods can clear up some of the subtler effects people try to take into account. The first half was about another gravitational application, that of using amplitudes methods to compute the correlations of galaxy structures in the sky, a field where it looks like a lot of progress can be made. Finally, Buonanno gave the kind of talk she’s given a few times at these conferences, a talk that puts these methods in context, explaining how amplitudes results are packaged with other types of calculations into the Effective-One-Body framework which then is more directly used at LIGO. This year’s talk went into more detail about what the predictions are actually used for, which I appreciated. I hadn’t realized that there have been a handful of black hole collisions discovered by other groups from LIGO’s data, a win for open science! Her slides had a nice diagram explaining what data from the gravitational wave is used to infer what black hole properties, quite a bit more organized than the statistical template-matching I was imagining. She explained the logic behind Bern’s statement that gravitational wave telescopes will need two more orders of magnitude, pointing out that that kind of precision is necessary to be sure that something that might appear to be a deviation from Einstein’s theory of gravity is not actually a subtle effect of known physics. Her method typically is adjusted to fit numerical simulations, but she shows that even without that adjustment they now fit the numerics quite well, thanks in part to contributions from amplitudes calculations.

Of the other talks that day, David Kosower’s was the only one that didn’t explicitly involve gravity. Instead, his talk focused on a more general question, namely how to find a well-defined basis of integrals for Feynman diagrams, which turns out to involve some rather subtle mathematics and geometry. This is a topic that my former boss Jake Bourjaily worked on in a different context for some time, and I’m curious whether there is any connection between the two approaches. Oliver Schlotterer gave the day’s second review talk, once again of the “actually a review” kind, covering a variety of recent developments in string theory amplitudes. These include some new pictures of how string theory amplitudes that correspond to Yang-Mills theories “square” to amplitudes involving gravity at higher loops and progress towards going past two loops, the current state of the art for most string amplitude calculations. (For the experts: this does not involve taking the final integral over the moduli space, which is still a big unsolved problem.) He also talked about progress by Sebastian Mizera and collaborators in understanding how the integrals that show up in string theory make sense in the complex plane. This is a problem that people had mostly managed to avoid dealing with because of certain simplifications in the calculations people typically did (no moduli space integration, expansion in the string length), but taking things seriously means confronting it, and Mizera and collaborators found a novel solution to the problem that has already passed a lot of checks. Finally, Tobias Hansen’s talk also related to string theory, specifically in anti-de-Sitter space, where the duality between string theory and N=4 super Yang-Mills lets him and his collaborators do Yang-Mills calculations and see markedly stringy-looking behavior.

Friday began with Kevin Costello, whose not-really-a-review talk dealt with his work with Natalie Paquette showing that one can use an exactly-solvable system to learn something about QCD. This only works for certain rather specific combinations of particles: for example, in order to have three colors of quarks, they need to do the calculation for nine flavors. Still, they managed to do a calculation with this method that had not previously been done with more traditional means, and to me it’s impressive that anything like this works for a theory without supersymmetry. Mina Himwich and Diksha Jain both had talks related to a topic of current interest, “celestial” conformal field theory, a picture that tries to apply ideas from holography in which a theory on the boundary of a space fully describes the interior, to the “boundary” of flat space, infinitely far away. Himwich talked about a symmetry observed in that research program, and how that symmetry can be seen using more normal methods, which also lead to some suggestions of how the idea might be generalized. Jain likewise covered a different approach, one in which one sets artificial boundaries in flat space and sees what happens when those boundaries move.

Yifei He described progress in the modern S-matrix bootstrap approach. Previously, this approach had gotten quite general constraints on amplitudes. She tries to do something more specific, and predict the S-matrix for scattering of pions in the real world. By imposing compatibility with knowledge from low energies and high energies, she was able to find a much more restricted space of consistent S-matrices, and these turn out to actually match pretty well to experimental results. Mathieu Giroux addresses an important question for a variety of parts of amplitudes research, how to predict the singularities of Feynman diagrams. He explored a recursive approach to solving Landau’s equations for these singularities, one which seems impressively powerful, in one case being able to find a solution that in text form is approximately the length of Harry Potter. Finally, Juan Maldacena closed the conference by talking about some progress he’s made towards an old idea, that of defining M theory in terms of a theory involving actual matrices. This is a very challenging thing to do, but he is at least able to tackle the simplest possible case, involving correlations between three observations. This had a known answer, so his work serves mostly as a confirmation that the original idea makes sense at at least this level.

Gravity-Defying Theories

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Universal gravitation was arguably Newton’s greatest discovery. Newton realized that the same laws could describe the orbits of the planets and the fall of objects on Earth, that bodies like the Moon can be fully understood only if you take into account both the Earth and the Sun’s gravity. In a Newtonian world, every mass attracts every other mass in a tiny, but detectable way.

Einstein, in turn, explained why. In Einstein’s general theory of relativity, gravity comes from the shape of space and time. Mass attracts mass, but energy affects gravity as well. Anything that can be measured has a gravitational effect, because the shape of space and time is nothing more than the rules by which we measure distances and times. So gravitation really is universal, and has to be universal.

…except when it isn’t.

It turns out, physicists can write down theories with some odd properties. Including theories where things are, in a certain sense, immune to gravity.

The story started with two mathematicians, Shiing-Shen Chern and Jim Simons. Chern and Simons weren’t trying to say anything in particular about physics. Instead, they cared about classifying different types of mathematical space. They found a formula that, when added up over one of these spaces, counted some interesting properties of that space. A bit more specifically, it told them about the space’s topology: rough details, like the number of holes in a donut, that stay the same even if the space is stretched or compressed. Their formula was called the Chern-Simons Form.

The physicist Albert Schwarz saw this Chern-Simons Form, and realized it could be interpreted another way. He looked at it as a formula describing a quantum field, like the electromagnetic field, describing how the field’s energy varied across space and time. He called the theory describing the field Chern-Simons Theory, and it was one of the first examples of what would come to be known as topological quantum field theories.

In a topological field theory, every question you might want to ask can be answered in a topological way. Write down the chance you observe the fields at particular strengths in particular places, and you’ll find that the answer you get only depends on the topology of the space the fields occupy. The answers are the same if the space is stretched or squished together. That means that nothing you ask depends on the details of how you measure things, that nothing depends on the detailed shape of space and time. Your theory is, in a certain sense, independent of gravity.

Others discovered more theories of this kind. Edward Witten found theories that at first looked like they depend on gravity, but where the gravity secretly “cancels out”, making the theory topological again. It turned out that there were many ways to “twist” string theory to get theories of this kind.

Our world is for the most part not described by a topological theory, gravity matters! (Though it can be a good approximation for describing certain materials.) These theories are most useful, though, in how they allow physicists and mathematicians to work together. Physicists don’t have a fully mathematically rigorous way of defining most of their theories, just a series of approximations and an overall picture that’s supposed to tie them together. For a topological theory, though, that overall picture has a rigorous mathematical meaning: it counts topological properties! As such, topological theories allow mathematicians to prove rigorous results about physical theories. It means they can take a theory of quantum fields or strings that has a particular property that physicists are curious about, and find a version of that property that they can study in fully mathematical rigorous detail. It’s been a boon both to mathematicians interested in topology, and to physicists who want to know more about their theories.

So while you won’t have antigravity boots any time soon, theories that defy gravity are still useful!

Book Review: The Case Against Reality

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Nima Arkani-Hamed shows up surprisingly rarely in popular science books. A major figure in my former field, Nima is extremely quotable (frequent examples include “spacetime is doomed” and “the universe is not a crappy metal”), but those quotes don’t seem to quite have reached the popular physics mainstream. He’s been interviewed in books by physicists, and has a major role in one popular physics book that I’m aware of. From this scattering of mentions, I was quite surprised to hear of another book where he makes an appearance: not a popular physics book at all, but a popular psychology book: Donald Hoffman’s The Case Against Reality. Naturally, this meant I had to read it.

Then, I saw the first quote on the back cover…or specifically, who was quoted.

Seeing that, I settled in for a frustrating read.

A few pages later, I realized that this, despite his endorsement, is not a Deepak Chopra kind of book. Hoffman is careful in some valuable ways. Specifically, he has a philosopher’s care, bringing up objections and potential holes in his arguments. As a result, the book wasn’t frustrating in the way I expected.

It was even more frustrating, actually. But in an entirely different way.

When a science professor writes a popular book, the result is often a kind of ungainly Frankenstein. The arguments we want to make tend to be better-suited to shorter pieces, like academic papers, editorials, and blog posts. To make these into a book, we have to pad them out. We stir together all the vaguely related work we’ve done, plus all the best-known examples from other peoples’ work, trying (often not all that hard) to make the whole sound like a cohesive story. Read enough examples, and you start to see the joints between the parts.

Hoffman is ostensibly trying to tell a single story. His argument is that the reality we observe, of objects in space and time, is not the true reality. It is a convenient reality, one that has led to our survival, but evolution has not (and as he argues, cannot) let us perceive the truth. Instead, he argues that the true reality is consciousness: a world made up of conscious beings interacting with each other, with space, time, and all the rest emerging as properties of those interactions.

That certainly sounds like it could be one, cohesive argument. In practice, though, it is three, and they don’t fit together as well as he’d hope.

Hoffman is trained as a psychologist. As such, one of the arguments is psychological: that research shows that we mis-perceive the world in service of evolutionary fitness.

Hoffman is a cognitive scientist, and while many cognitive scientists are trained as psychologists, others are trained as philosophers. As such, one of his arguments is philosophical: that the contents of consciousness can never be explained by relations between material objects, and that evolution, and even science, systematically lead us astray.

Finally, Hoffman has evidently been listening to and reading the work of some physicists, like Nima and Carlo Rovelli. As such, one of his arguments is physical: that physicists believe that space and time are illusions and that consciousness may be fundamental, and that the conclusions of the book lead to his own model of the basic physical constituents of the world.

The book alternates between these three arguments, so rather than in chapter order, I thought it would be better to discuss each argument in its own section.

The Psychological Argument

Sometimes, when two academics get into a debate, they disagree about what’s true. Two scientists might argue about whether an experiment was genuine, whether the statistics back up a conclusion, or whether a speculative theory is actually consistent. These are valuable debates, and worth reading about if you want to learn something about the nature of reality.

Sometimes, though, two debating academics agree on what’s true, and just disagree on what’s important. These debates are, at best, relevant to other academics and funders. They are not generally worth reading for anybody else, and are often extremely petty and dumb.

Hoffman’s psychological argument, regrettably, is of the latter kind. He would like to claim it’s the former, and to do so he marshals a host of quotes from respected scientists that claim that human perception is veridical: that what we perceive is real, courtesy of an evolutionary process that would have killed us off if it wasn’t. From that perspective, every psychological example Hoffman gives is a piece of counter-evidence, a situation where evolution doesn’t just fail to show us the true nature of reality, but actively hides reality from us.

The problem is that, if you actually read the people Hoffman quotes, they’re clearly not making the extreme point he claims. These people are psychologists, and all they are arguing is that perception is veridical in a particular, limited way. They argue that we humans are good at estimating distances or positions of objects, or that we can see a wide range of colors. They aren’t making some sort of philosophical point about those distances or positions or colors being how the world “really is”, nor are they claiming that evolution never makes humans mis-perceive.

Instead, they, and thus Hoffman, are arguing about importance. When studying humans, is it more useful to think of us as perceiving the world as it is? Or is it more useful to think of evolution as tricking us? Which happens more often?

The answers to each of those questions have to be “it depends”. Neither answer can be right all the time. At most then, this kind of argument can convince one academic to switch from researching in one way to researching in another, by saying that right now one approach is a better strategy. It can’t tell us anything more.

If the argument Hoffman is trying to get across here doesn’t matter, are there other reasons to read this part?

Popular psychology books tend to re-use a few common examples. There are some good ones, so if you haven’t read such a book you probably should read a couple, just to hear about them. For example, Hoffman tells the story of the split-brain patients, which is definitely worth being aware of.

(Those of you who’ve heard that story may be wondering how the heck Hoffman squares it with his idea of consciousness as fundamental. He actually does have a (weird) way to handle this, so read on.)

The other examples come from Hoffman’s research, and other research in his sub-field. There are stories about what optical illusions tell us about our perception, about how evolution primes us to see different things as attractive, and about how advertisers can work with attention.

These stories would at least be a source of a few more cool facts, but I’m a bit wary. The elephant in the room here is the replication crisis. Paper after paper in psychology has turned out to be a statistical mirage, accidental successes that fail to replicate in later experiments. This can happen without any deceit on the part of the psychologist, it’s just a feature of how statistics are typically done in the field.

Some psychologists make a big deal about the replication crisis: they talk about the statistical methods they use, and what they do to make sure they’re getting a real result. Hoffman talks a bit about tricks to rule out other explanations, but mostly doesn’t focus on this kind of thing.. This doesn’t mean he’s doing anything wrong: it might just be it’s off-topic. But it makes it a bit harder to trust him, compared to other psychologists who do make a big deal about it.

The Philosophical Argument

Hoffman structures his book around two philosophical arguments, one that appears near the beginning and another that, as he presents it, is the core thesis of the book. He calls both of these arguments theorems, a naming choice sure to irritate mathematicians and philosophers alike, but the mathematical content in either is for the most part not the point: in each case, the philosophical setup is where the arguments get most of their strength.

The first of these arguments, called The Scrambling Theorem, is set up largely as background material: not his core argument, but just an entry into the overall point he’s making. I found it helpful as a way to get at his reasoning style, the sorts of things he cares about philosophically and the ones he doesn’t.

The Scrambling Theorem is meant to weigh in on the debate over a thought experiment called the Inverted Spectrum, which in turn weighs on the philosophical concept of qualia. The Inverted Spectrum asks us to imagine someone who sees the spectrum of light inverted compared to how we see it, so that green becomes red and red becomes green, without anything different about their body or brain. Such a person would learn to refer to colors the same ways that we do, still referring to red blood even though they see what we see when we see green grass. Philosophers argue that, because we can imagine this, the “qualia” we see in color, like red or green, are distinct from their practical role: they are images in the mind’s eye that can be compared across minds, but do not correspond to anything we have yet characterized scientifically in the physical world.

As a response, other philosophers argued that you can’t actually invert the spectrum. Colors aren’t really a wheel, we can distinguish, for example, more colors between red and blue than between green and yellow. Just flipping colors around would have detectable differences that would have to have physical implications, you can’t just swap qualia and nothing else.

The Scrambling Theorem is in response to this argument. Hoffman argues that, while you can’t invert the spectrum, you can scramble it. By swapping not only the colors, but the relations between them, you can arrange any arbitrary set of colors however else you’d like. You can declare that green not only corresponds to blood and not grass, but that it has more colors between it and yellow, perhaps by stealing them from the other side of the color wheel. If you’re already allowed to swap colors and their associations around, surely you can do this too, and change order and distances between them.

Believe it or not, I think Hoffman’s argument is correct, at least in its original purpose. You can’t respond to the Inverted Spectrum just by saying that colors are distributed differently on different sides of the color wheel. If you want to argue against the Inverted Spectrum, you need a better argument.

Hoffman’s work happens to suggest that better argument. Because he frames this argument in the language of mathematics, as a “theorem”, Hoffman’s argument is much more general than the summary I gave above. He is arguing that not merely can you scramble colors, but anything you like. If you want to swap electrons and photons, you can: just make your photons interact with everything the way electrons did, and vice versa. As long as you agree that the things you are swapping exist, according to Hoffman, you are free to exchange them and their properties any way you’d like.

This is because, to Hoffman, things that “actually exist” cannot be defined just in terms of their relations. An electron is not merely a thing that repels other electrons and is attracted to protons and so on, it is a thing that “actually exists” out there in the world. (Or, as he will argue, it isn’t really. But that’s because in the end he doesn’t think electrons exist.)

(I’m tempted to argue against this with a mathematical object like group elements. Surely the identity element of a group is defined by its relations? But I think he would argue identity elements of groups don’t actually exist.)

In the end, Hoffman is coming from a particular philosophical perspective, one common in modern philosophers of metaphysics, the study of the nature of reality. From this perspective, certain things exist, and are themselves by necessity. We cannot ask what if a thing were not itself. For example, in this perspective it is nonsense to ask what if Superman was not Clark Kent, because the two names refer to the same actually existing person.

(If, you know, Superman actually existed.)

Despite the name of the book, Hoffman is not actually making a case against reality in general. He very much seems to believe in this type of reality, in the idea that there are certain things out there that are real, independent of any purely mathematical definition of their properties. He thinks they are different things than you think they are, but he definitely thinks there are some such things, and that it’s important and scientifically useful to find them.

Hoffman’s second argument is, as he presents it, the core of the book. It’s the argument that’s supposed to show that the world is almost certainly not how we perceive it, even through scientific instruments and the scientific method. Once again, he calls it a theorem: the Fitness Beats Truth theorem.

The Fitness Beats Truth argument begins with a question: why should we believe what we see? Why do we expect that the things we perceive should be true?

In Hoffman’s mind, the only answer is evolution. If we perceived the world inaccurately, we would die out, replaced by creatures that perceived the world better than we did. You might think we also have evidence from biology, chemistry, and physics: we can examine our eyes, test them against cameras, see how they work and what they can and can’t do. But to Hoffman, all of this evidence may be mistaken, because to learn biology, chemistry, and physics we must first trust that we perceive the world correctly to begin with. Evolution, though, doesn’t rely on any of that. Even if we aren’t really bundles of cells replicating through DNA and RNA, we should still expect something like evolution, some process by which things differ, are selected, and reproduce their traits differently in the next generation. Such things are common enough, and general enough, that one can (handwavily) expect them through pure reason alone.

But, says Hoffman’s psychology experience, evolution tricks us! We do mis-perceive, and systematically, in ways that favor our fitness over reality. And so Hoffman asks, how often should we expect this to happen?

The Fitness Beats Truth argument thinks of fitness as randomly distributed: some parts of reality historically made us more fit, some less. This distribution could match reality exactly, so that for any two things that are actually different, they will make us fit in different ways. But it doesn’t have to. There might easily be things that are really very different from each other, but which are close enough from a fitness perspective that to us they seem exactly the same.

The “theorem” part of the argument is an attempt to quantify this. Hoffman imagines a pixelated world, and asks how likely it is that a random distribution of fitness matches a random distribution of pixels. This gets extremely unlikely for a world of any reasonable size, for pretty obvious reasons. Thus, Hoffman concludes: in a world with evolution, we should almost always expect it to hide something from us. The world, if it has any complexity at all, has an almost negligible probability of being as we perceive it.

On one level, this is all kind of obvious. Evolution does trick us sometimes, just as it tricks other animals. But Hoffman is trying to push this quite far, to say that ultimately our whole picture of reality, not just our eyes and ears and nose but everything we see with microscopes and telescopes and calorimeters and scintillators, all of that might be utterly dramatically wrong. Indeed, we should expect it to be.

In this house, we tend to dismiss the Cartesian Demon. If you have an argument that makes you doubt literally everything, then it seems very unlikely you’ll get anything useful from it. Unlike Descartes’s Demon, Hoffman thinks we won’t be tricked forever. The tricks evolution plays on us mattered in our ancestral environment, but over time we move to stranger and stranger situations. Eventually, our fitness will depend on something new, and we’ll need to learn something new about reality.

This means that ultimately, despite the skeptical cast, Hoffman’s argument fits with the way science already works. We are, very much, trying to put ourselves in new situations and test whether our evolved expectations still serve us well or whether we need to perceive things anew. That is precisely what we in science are always doing, every day. And as we’ll see in the next section, whatever new things we have to learn have no particular reason to be what Hoffman thinks they should be.

But while it doesn’t really matter, I do still want to make one counter-argument to Fitness Beats Truth. Hoffman considers a random distribution of fitness, and asks what the chance is that it matches truth. But fitness isn’t independent of truth, and we know that not just from our perception, but from deeper truths of physics and mathematics. Fitness is correlated with truth, fitness often matches truth, for one key reason: complex things are harder than simple things.

Imagine a creature evolving an eye. They have a reason, based on fitness, to need to know where their prey is moving. If evolution was a magic wand, and chemistry trivial, it would let them see their prey, and nothing else. But evolution is not magic, and chemistry is not trivial. The easiest thing for this creature to see is patches of light and darkness. There are many molecules that detect light, because light is a basic part of the physical world. To detect just prey, you need something much more complicated, molecules and cells and neurons. Fitness imposes a cost, and it means that the first eyes that evolve are spots, detecting just light and darkness.

Hoffman asks us not to assume that we know how eyes work, that we know how chemistry works, because we got that knowledge from our perceptions. But the nature of complexity and simplicity, entropy and thermodynamics and information, these are things we can approach through pure thought, as much as evolution. And those principles tell us that it will always be easier for an organism to perceive the world as it truly is than not, because the world is most likely simple and it is most likely the simplest path to perceive it directly. When benefits get high enough, when fitness gets strong enough, we can of course perceive the wrong thing. But if there is only a small fitness benefit to perceiving something incorrectly, then simplicity will win out. And by asking simpler and simpler questions, we can make real durable scientific progress towards truth.

The Physical Argument

So if I’m not impressed by the psychology or the philosophy, what about the part that motivated me to read the book in the first place, the physics?

Because this is, in a weird and perhaps crackpot way, a physics book. Hoffman has a specific idea, more specific than just that the world we perceive is an evolutionary illusion, more specific than that consciousness cannot be explained by the relations between physical particles. He has a proposal, based on these ideas, one that he thinks might lead to a revolutionary new theory of physics. And he tries to argue that physicists, in their own way, have been inching closer and closer to his proposal’s core ideas.

Hoffman’s idea is that the world is made, not of particles or fields or anything like that, but of conscious agents. You and I are, in this picture, certainly conscious agents, but so are the sources of everything we perceive. When we reach out and feel a table, when we look up and see the Sun, those are the actions of some conscious agent intruding on our perceptions. Unlike panpsychists, who believe that everything in the world is conscious, Hoffman doesn’t believe that the Sun itself is conscious, or is made of conscious things. Rather, he thinks that the Sun is an evolutionary illusion that rearranges our perceptions in a convenient way. The perceptions still come from some conscious thing or set of conscious things, but unlike in panpsychism they don’t live in the center of our solar system, or in any other place (space and time also being evolutionary illusions in this picture). Instead, they could come from something radically different that we haven’t imagined yet.

Earlier, I mentioned split brain patients. For anyone who thinks of conscious beings as fundamental, split brain patients are a challenge. These are people who, as a treatment for epilepsy, had the bridge between the two halves of their brain severed. The result is eerily as if their consciousness was split in two. While they only express one train of thought, that train of thought seems to only correspond to the thoughts of one side of their brain, controlling only half their body. The other side, controlling the other half of their body, appears to have different thoughts, different perceptions, and even different opinions, which are made manifest when instead of speaking they use that side of their body to gesture and communicate. While some argue that these cases are over-interpreted and don’t really show what they’re claimed to, Hoffman doesn’t. He accepts that these split-brain patients genuinely have their consciousness split in two.

Hoffman thinks this isn’t a problem because for him, conscious agents can be made up of other conscious agents. Each of us is conscious, but we are also supposed to be made up of simpler conscious agents. Our perceptions and decisions are not inexplicable, but can be explained in terms of the interactions of the simpler conscious entities that make us up, each one communicating with the others.

Hoffman speculates that everything is ultimately composed of the simplest possible conscious agents. For him, a conscious agent must do two things: perceive, and act. So the simplest possible agent perceives and acts in the simplest possible way. They perceive a single bit of information: 0 or 1, true or false, yes or no. And they take one action, communicating a different bit of information to another conscious agent: again, 0 or 1, true or false, yes or no.

Hoffman thinks that this could be the key to a new theory of physics. Instead of thinking about the world as composed of particles and fields, think about it as composed of these simple conscious agents, each one perceiving and communicating one bit at a time.

Hoffman thinks this, in part, because he sees physics as already going in this direction. He’s heard that “spacetime is doomed”, he’s heard that quantum mechanics is contextual and has no local realism, he’s heard that quantum gravity researchers think the world might be a hologram and space-time has a finite number of bits. This all “rhymes” enough with his proposal that he’s confident physics has his back.

Hoffman is trained in psychology. He seems to know his philosophy, at least enough to engage with the literature there. But he is absolutely not a physicist, and it shows. Time and again it seems like he relies on “pop physics” accounts that superficially match his ideas without really understanding what the physicists are actually talking about.

He keeps up best when it comes to interpretations of quantum mechanics, a field where concepts from philosophy play a meaningful role. He covers the reasons why quantum mechanics keeps philosophers up at night: Bell’s Theorem, which shows that a theory that matches the predictions of quantum mechanics cannot both be “realist”, with measurements uncovering pre-existing facts about the world, and “local”, with things only influencing each other at less than the speed of light, the broader notion of contextuality, where measured results are dependent on which other measurements are made, and the various experiments showing that both of these properties hold in the real world.

These two facts, and their implications, have spawned a whole industry of interpretations of quantum mechanics, where physicists and philosophers decide which side of various dilemmas to take and how to describe the results. Hoffman quotes a few different “non-realist” interpretations: Carlo Rovelli’s Relational Quantum Mechanics, Quantum Bayesianism/QBism, Consistent Histories, and whatever Chris Fields is into. These are all different from one another, which Hoffman is aware of. He just wants to make the case that non-realist interpretations are reasonable, that the physicists collectively are saying “maybe reality doesn’t exist” just like he is.

The problem is that Hoffman’s proposal is not, in the quantum mechanics sense, non-realist. Yes, Hoffman thinks that the things we observe are just an “interface”, that reality is really a network of conscious agents. But in order to have a non-realist interpretation, you need to also have other conscious agents not be real. That’s easily seen from the old “Wigner’s friend” thought experiment, where you put one of your friends in a Schrodinger’s cat-style box. Just as Schrodinger’s cat can be both alive and dead, your friend can both have observed something and not have observed it, or observed something and observed something else. The state of your friend’s mind, just like everything else in a non-realist interpretation, doesn’t have a definite value until you measure it.

Hoffman’s setup doesn’t, and can’t, work that way. His whole philosophical project is to declare that certain things exist and others don’t: the sun doesn’t exist, conscious agents do. In a non-realist interpretation, the sun and other conscious agents can both be useful descriptions, but ultimately nothing “really exists”. Science isn’t a catalogue of what does or doesn’t “really exist”, it’s a tool to make predictions about your observations.

Hoffman gets even more confused when he gets to quantum gravity. He starts out with a common misconception: that the Planck length represents the “pixels” of reality, sort of like the pixels of your computer screen, which he uses to support his “interface” theory of consciousness. This isn’t really the right way to think about it the Planck length, though, and certainly isn’t what the people he’s quoting have in mind. The Planck length is a minimum scale in that space and time stop making sense as one approaches it, but that’s not necessarily because space and time are made up of discrete pixels. Rather, it’s because as you get closer to the Planck length, space and time stop being the most convenient way to describe things. For a relatively simple example of how this can work, see my post here.

From there, he reflects on holography: the discovery that certain theories in physics can be described equally well by what is happening on their boundary as by their interior, the way that a 2D page can hold all the information for an apparently 3D hologram. He talks about the Bekenstein bound, the conjecture that there is a maximum amount of information needed to describe a region of space, proportional not to the volume of the region but to its area. For Hoffman, this feels suspiciously like human vision: if we see just a 2D image of the world, could that image contain all the information needed to construct that world? Could the world really be just what we see?

In a word, no.

On the physics side, the Bekenstein bound is a conjecture, and one that doesn’t always hold. A more precise version that seems to hold more broadly, called the Bousso bound, works by demanding the surface have certain very specific geometric properties in space-time, properties not generally shared by the retinas of our eyes.

But it even fails in Hoffman’s own context, once we remember that there are other types of perception than vision. When we hear, we don’t detect a 2D map, but a 1D set of frequencies, put in “stereo” by our ears. When we feel pain, we can feel it in any part of our body, essentially a 3D picture since it goes inwards as well. Nothing about human perception uniquely singles out a 2D surface.

There is actually something in physics much closer to what Hoffman is imagining, but it trades on a principle Hoffman aspires to get rid of: locality. We’ve known since Einstein that you can’t change the world around you faster than the speed of light. Quantum mechanics doesn’t change that, despite what you may have heard. More than that, simultaneity is relative: two distant events might be at the same time in your reference frame, but for someone else one of them might be first, or the other one might be, there is no one universal answer.

Because of that, if you want to think about things happening one by one, cause following effect, actions causing consequences, then you can’t think of causes or actions as spread out in space. You have to think about what happens at a single point: the location of an imagined observer.

Once you have this concept, you can ask whether describing the world in terms of this single observer works just as well as describing it in terms of a wide open space. And indeed, it actually can do well, at least under certain conditions. But one again, this really isn’t how Hoffman is doing things: he has multiple observers all real at the same time, communicating with each other in a definite order.

In general, a lot of researchers in quantum gravity think spacetime is doomed. They think things are better described in terms of objects with other properties and interactions, with space and time as just convenient approximations for a more complicated reality. They get this both from observing properties of the theories we already have, and from thought experiments showing where those theories cause problems.

Nima, the most catchy of these quotable theorists, is approaching the problem from the direction of scattering amplitudes: the calculations we do to find the probability of observations in particle physics. Each scattering amplitude describes a single observation: what someone far away from a particle collision can measure, independent of any story of what might have “actually happened” to the particles in between. Nima’s goal is to describe these amplitudes purely in terms of those observations, to get rid of the “story” that shows up in the middle as much as possible.

The other theorists have different goals, but have this in common: they treat observables as their guide. They look at the properties that a single observer’s observations can have, and try to take a fresh view, independent of any assumptions about what happens in between.

This key perspective, this key insight, is what Hoffman is missing throughout this book. He has read what many physicists have to say, but he does not understand why they are saying it. His book is titled The Case Against Reality, but he merely trades one reality for another. He stops short of the more radical, more justified case against reality: that “reality”, that thing philosophers argue about and that makes us think we can rule out theories based on pure thought, is itself the wrong approach: that instead of trying to characterize an idealized real world, we are best served by focusing on what we can do.

One thing I didn’t do here is a full critique of Hoffman’s specific proposal, treating it as a proposed theory of physics. That would involve quite a bit more work, on top of what has turned out to be a very long book review. I would need to read not just his popular description, but the actual papers where he makes his case and lays out the relevant subtleties. Since I haven’t done that, I’ll end with a few questions: things that his proposal will need to answer if it aspires to be a useful idea for physics.

  • Are the networks of conscious agents he proposes Turing-complete? In other words, can they represent any calculation a computer can do? If so, they aren’t a useful idea for physics, because you could imagine a network of conscious agents to reproduce any theory you want. The idea wouldn’t narrow things down to get us closer to a useful truth. This was also one of the things that made me uncomfortable with the Wolfram Physics Project.
  • What are the conditions that allow a network of simple conscious agents to make up a bigger conscious agent? Do those conditions depend meaningfully on the network’s agents being conscious, or do they just have to pass messages? If the latter, then Hoffman is tacitly admitting you can make a conscious agent out of non-conscious agents, even if he insists this is philosophically impossible.
  • How do you square this network with relativity and quantum mechanics? Is there a set time, an order in which all the conscious agents communicate with each other? If so, how do you square that with the relativity of simultaneity? Are the agents themselves supposed to be able to be put in quantum states, or is quantum mechanics supposed to emerge from a theory of classical agents?
  • How does evolution fit in here? A bit part of Hoffman’s argument was supported by the universality of the evolutionary algorithm. In order for evolution to matter for your simplest agents, they need to be able to be created or destroyed. But then they have more than two actions: not just 0 and 1, but 0, 1, and cease to exist. So you could have an even simpler agent that has just two bits.

Amplitudes 2023 Retrospective

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I’m back from CERN this week, with a bit more time to write, so I thought I’d share some thoughts about last week’s Amplitudes conference.

One thing I got wrong in last week’s post: I’ve now been told only 213 people actually showed up in person, as opposed to the 250-ish estimate I had last week. This may seem fewer than Amplitudes in Prague had, but it seems likely they had a few fewer show up than appeared on the website. Overall, the field is at least holding steady from year to year, and definitely has grown since the pandemic (when 2019’s 175 was already a very big attendance).

It was cool having a conference in CERN proper, surrounded by the history of European particle physics. The lecture hall had an abstract particle collision carved into the wood, and the visitor center would in principle have had Standard Model coffee mugs were they not sold out until next May. (There was still enough other particle physics swag, Swiss chocolate, and Swiss chocolate that was also particle physics swag.) I’d planned to stay on-site at the CERN hostel, but I ended up appreciated not doing that: the folks who did seemed to end up a bit cooped up by the end of the conference, even with the conference dinner as a chance to get out.

Past Amplitudes conferences have had associated public lectures. This time we had a not-supposed-to-be-public lecture, a discussion between Nima Arkani-Hamed and Beate Heinemann about the future of particle physics. Nima, prominent as an amplitudeologist, also has a long track record of reasoning about what might lie beyond the Standard Model. Beate Heinemann is an experimentalist, one who has risen through the ranks of a variety of different particle physics experiments, ending up well-positioned to take a broad view of all of them.

It would have been fun if the discussion erupted into an argument, but despite some attempts at provocative questions from the audience that was not going to happen, as Beate and Nima have been friends for a long time. Instead, they exchanged perspectives: on what’s coming up experimentally, and what theories could explain it. Both argued that it was best to have many different directions, a variety of experiments covering a variety of approaches. (There wasn’t any evangelism for particular experiments, besides a joking sotto voce mention of a muon collider.) Nima in particular advocated that, whether theorist or experimentalist, you have to have some belief that what you’re doing could lead to a huge breakthrough. If you think of yourself as just a “foot soldier”, covering one set of checks among many, then you’ll lose motivation. I think Nima would agree that this optimism is irrational, but necessary, sort of like how one hears (maybe inaccurately) that most new businesses fail, but someone still needs to start businesses.

Michelangelo Mangano’s talk on Thursday covered similar ground, but with different emphasis. He agrees that there are still things out there worth discovering: that our current model of the Higgs, for instance, is in some ways just a guess: a simplest-possible answer that doesn’t explain as much as we’d like. But he also emphasized that Standard Model physics can be “new physics” too. Just because we know the model doesn’t mean we can calculate its consequences, and there are a wealth of results from the LHC that improve our models of protons, nuclei, and the types of physical situations they partake in, without changing the Standard Model.

We saw an impressive example of this in Gregory Korchemsky’s talk on Wednesday. He presented an experimental mystery, an odd behavior in the correlation of energies of jets of particles at the LHC. These jets can include a very large number of particles, enough to make it very hard to understand them from first principles. Instead, Korchemsky tried out our field’s favorite toy model, where such calculations are easier. By modeling the situation in the limit of a very large number of particles, he was able to reproduce the behavior of the experiment. The result was a reminder of what particle physics was like before the Standard Model, and what it might become again: partial models to explain odd observations, a quest to use the tools of physics to understand things we can’t just a priori compute.

On the other hand, amplitudes does do a priori computations pretty well as well. Fabrizio Caola’s talk opened the conference by reminding us just how much our precise calculations can do. He pointed out that the LHC has only gathered 5% of its planned data, and already it is able to rule out certain types of new physics to fairly high energies (by ruling out indirect effects, that would show up in high-precision calculations). One of those precise calculations featured in the next talk, by Guilio Gambuti. (A FORM user, his diagrams were the basis for the header image of my Quanta article last winter.) Tiziano Peraro followed up with a technique meant to speed up these kinds of calculations, a trick to simplify one of the more computationally intensive steps in intersection theory.

The rest of Monday was more mathematical, with talks by Zeno Capatti, Jaroslav Trnka, Chia-Kai Kuo, Anastasia Volovich, Francis Brown, Michael Borinsky, and Anna-Laura Sattelberger. Borinksy’s talk felt the most practical, a refinement of his numerical methods complete with some actual claims about computational efficiency. Francis Brown discussed an impressively powerful result, a set of formulas that manages to unite a variety of invariants of Feynman diagrams under a shared explanation.

Tuesday began with what I might call “visitors”: people from adjacent fields with an interest in amplitudes. Alday described how the duality between string theory in AdS space and super Yang-Mills on the boundary can be used to get quite concrete information about string theory, calculating how the theory’s amplitudes are corrected by the curvature of AdS space using a kind of “bootstrap” method that felt nicely familiar. Tim Cohen talked about a kind of geometric picture of theories that extend the Standard Model, including an interesting discussion of whether it’s really “geometric”. Marko Simonovic explained how the integration techniques we develop in scattering amplitudes can also be relevant in cosmology, especially for the next generation of “sky mappers” like the Euclid telescope. This talk was especially interesting to me since this sort of cosmology has a significant presence at CEA Paris-Saclay. Along those lines an interesting paper, “Cosmology meets cohomology”, showed up during the conference. I haven’t had a chance to read it yet!

Just before lunch, we had David Broadhurst give one of his inimitable talks, complete with number theory, extremely precise numerics, and literary and historical references (apparently, Källén died flying his own plane). He also remedied a gap in our whimsically biological diagram naming conventions, renaming the pedestrian “double-box” as a (in this context, Orwellian) lobster. Karol Kampf described unusual structures in a particular Effective Field Theory, while Henriette Elvang’s talk addressed what would become a meaningful subtheme of the conference, where methods from the mathematical field of optimization help amplitudes researchers constrain the space of possible theories. Giulia Isabella covered another topic on this theme later in the day, though one of her group’s selling points is managing to avoid quite so heavy-duty computations.

The other three talks on Tuesday dealt with amplitudes techniques for gravitational wave calculations, as did the first talk on Wednesday. Several of the calculations only dealt with scattering black holes, instead of colliding ones. While some of the results can be used indirectly to understand the colliding case too, a method to directly calculate behavior of colliding black holes came up again and again as an important missing piece.

The talks on Wednesday had to start late, owing to a rather bizarre power outage (the lights in the room worked fine, but not the projector). Since Wednesday was the free afternoon (home of quickly sold-out CERN tours), this meant there were only three talks: Veneziano’s talk on gravitational scattering, Korchemsky’s talk, and Nima’s talk. Nima famously never finishes on time, and this time attempted to control his timing via the surprising method of presenting, rather than one topic, five “abstracts” on recent work that he had not yet published. Even more surprisingly, this almost worked, and he didn’t run too ridiculously over time, while still managing to hint at a variety of ways that the combinatorial lessons behind the amplituhedron are gradually yielding useful perspectives on more general realistic theories.

Thursday, Andrea Puhm began with a survey of celestial amplitudes, a topic that tries to build the same sort of powerful duality used in AdS/CFT but for flat space instead. They’re gradually tackling the weird, sort-of-theory they find on the boundary of flat space. The two next talks, by Lorenz Eberhardt and Hofie Hannesdottir, shared a collaborator in common, namely Sebastian Mizera. They also shared a common theme, taking a problem most people would have assumed was solved and showing that approaching it carefully reveals extensive structure and new insights.

Cristian Vergu, in turn, delved deep into the literature to build up a novel and unusual integration method. We’ve chatted quite a bit about it at the Niels Bohr Institute, so it was nice to see it get some attention on the big stage. We then had an afternoon of trips beyond polylogarithms, with talks by Anne Spiering, Christoph Nega, and Martijn Hidding, each pushing the boundaries of what we can do with our hardest-to-understand integrals. Einan Gardi and Ruth Britto finished the day, with a deeper understanding of the behavior of high-energy particles and a new more mathematically compatible way of thinking about “cut” diagrams, respectively.

On Friday, João Penedones gave us an update on a technique with some links to the effective field theory-optimization ideas that came up earlier, one that “bootstraps” whole non-perturbative amplitudes. Shota Komatsu talked about an intriguing variant of the “planar” limit, one involving large numbers of particles and a slick re-writing of infinite sums of Feynman diagrams. Grant Remmen and Cliff Cheung gave a two-parter on a bewildering variety of things that are both surprisingly like, and surprisingly unlike, string theory: important progress towards answering the question “is string theory unique?”

Friday afternoon brought the last three talks of the conference. James Drummond had more progress trying to understand the symbol letters of supersymmetric Yang-Mills, while Callum Jones showed how Feynman diagrams can apply to yet another unfamiliar field, the study of vortices and their dynamics. Lance Dixon closed the conference without any Greta Thunberg references, but with a result that explains last year’s mystery of antipodal duality. The explanation involves an even more mysterious property called antipodal self-duality, so we’re not out of work yet!

At Amplitudes 2023 at CERN

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I’m at the big yearly conference of my sub-field this week, called Amplitudes. This year, surprisingly for the first time, it’s at the very appropriate location of CERN.

Somewhat overshadowed by the very picturesque Alps

Amplitudes keeps on growing. In 2019, we had 175 participants. We were on Zoom in 2020 and 2021, with many more participants, but that probably shouldn’t count. In Prague last year we had 222. This year, I’ve been told we have even more, something like 250 participants (the list online is bigger, but includes people joining on Zoom). We’ve grown due to new students, but also new collaborations: people from adjacent fields who find the work interesting enough to join along. This year we have mathematicians talking about D-modules, bootstrappers finding new ways to get at amplitudes in string theory, beyond-the-standard-model theorists talking about effective field theories, and cosmologists talking about the large-scale structure of the universe.

The talks have been great, from clear discussions of earlier results to fresh-off-the-presses developments, plenty of work in progress, and even one talk where the speaker’s opinion changed during the coffee break. As we’re at CERN, there’s also a through-line about the future of particle physics, with a chat between Nima Arkani-Hamed and the experimentalist Beate Heinemann on Tuesday and a talk by Michelangelo Mangano about the meaning of “new physics” on Thursday.

I haven’t had a ton of time to write, I keep getting distracted by good discussions! As such, I’ll do my usual thing, and say a bit more about specific talks in next week’s post.