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Book Review: The Case Against Reality

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.

Cabinet of Curiosities: The Deluxe Train Set

What’s a Cosmic String?

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Nowadays, we have telescopes that detect not just light, but gravitational waves. We’ve already learned quite a bit about astrophysics from these telescopes. They observe ripples coming from colliding black holes, giving us a better idea of what kinds of black holes exist in the universe. But the coolest thing a gravitational wave telescope could discover is something that hasn’t been seen yet: a cosmic string.

This art is from an article in Symmetry magazine which is, as far as I can tell, not actually about cosmic strings.

You might have heard of cosmic strings, but unless you’re a physicist you probably don’t know much about them. They’re a prediction, coming from cosmology, of giant string-like objects floating out in space.

That might sound like it has something to do with string theory, but it doesn’t actually have to, you can have these things without any string theory at all. Instead, you might have heard that cosmic strings are some kind of “cracks” or “wrinkles” in space-time. Some articles describe this as like what happens when ice freezes, cracks forming as water settles into a crystal.

That description, in terms of ice forming cracks between crystals, is great…if you’re a physicist who already knows how ice forms cracks between crystals. If you’re not, I’m guessing reading those kinds of explanations isn’t helpful. I’m guessing you’re still wondering why there ought to be any giant strings floating in space.

The real explanation has to do with a type of mathematical gadget physicists use, called a scalar field. You can think of a scalar field as described by a number, like a temperature, that can vary in space and time. The field carries potential energy, and that energy depends on what the scalar field’s “number” is. Left alone, the field settles into a situation with as little potential energy as it can, like a ball rolling down a hill. That situation is one of the field’s default values, something we call a “vacuum” value. Changing the field away from its vacuum value can take a lot of energy. The Higgs boson is one example of a scalar field. Its vacuum value is the value it has in day to day life. In order to make a detectable Higgs boson at the Large Hadron Collider, they needed to change the field away from its vacuum value, and that took a lot of energy.

In the very early universe, almost back at the Big Bang, the world was famously in a hot dense state. That hot dense state meant that there was a lot of energy to go around, so scalar fields could vary far from their vacuum values, pretty much randomly. As the universe expanded and cooled, there was less and less energy available for these fields, and they started to settle down.

Now, the thing about these default, “vacuum” values of a scalar field is that there doesn’t have to be just one of them. Depending on what kind of mathematical function the field’s potential energy is, there could be several different possibilities each with equal energy.

Let’s imagine a simple example, of a field with two vacuum values: +1 and -1. As the universe cooled down, some parts of the universe would end up with that scalar field number equal to +1, and some to -1. But what happens in between?

The scalar field can’t just jump from -1 to +1, that’s not allowed in physics. It has to pass through 0 in between. But, unlike -1 and +1, 0 is not a vacuum value. When the scalar field number is equal to 0, the field has more energy than it does when it’s equal to -1 or +1. Usually, a lot more energy.

That means the region of scalar field number 0 can’t spread very far: the further it spreads, the more energy it takes to keep it that way. On the other hand, the region can’t vanish altogether: something needs to happen to transition between the numbers -1 and +1.

The thing that happens is called a domain wall. A domain wall is a thin sheet, as thin as it can physically be, where the scalar field doesn’t take its vacuum value. You can roughly think of it as made up of the scalar field, a churning zone of the kind of bosons the LHC was trying to detect.

This sheet still has a lot of energy, bound up in the unusual value of the scalar field, like an LHC collision in every proton-sized chunk. As such, like any object with a lot of energy, it has a gravitational field. For a domain wall, the effect of this gravity would be very very dramatic: so dramatic, that we’re pretty sure they’re incredibly rare. If they were at all common, we would have seen evidence of them long before now!

Ok, I’ve shown you a wall, that’s weird, sure. What does that have to do with cosmic strings?

The number representing a scalar field doesn’t have to be a real number: it can be imaginary instead, or even complex. Now I’d like you to imagine a field with vacuum values on the unit circle, in the complex plane. That means that +1 and -1 are still vacuum values, but so are $e^{i \pi/2}$ , and $e^{3 i \pi/2}$ , and everything else you can write as $e^{i\theta}$ . However, 0 is still not a vacuum value. Neither is, for example, $2 e^{i\pi/3}$ .

With vacuum values like this, you can’t form domain walls. You can make a path between -1 and +1 that only goes through the unit circle, through $e^{i \pi/2}$ for example. The field will be at its vacuum value throughout, taking no extra energy.

However, imagine the different regions form a circle. In the picture above, suppose that the blue area at the bottom is at vacuum value -1 and red is at +1. You might have $e^{i \pi/2}$ in the green region, and $e^{3 i \pi/2}$ in the purple region, covering the whole circle smoothly as you go around.

Now, think about what happens in the middle of the circle. On one side of the circle, you have -1. On the other, +1. (Or, on one side $e^{i \pi/2}$ , on the other, $e^{3 i \pi/2}$ ). No matter what, different sides of the circle are not allowed to be next to each other, you can’t just jump between them. So in the very middle of the circle, something else has to happen.

Once again, that something else is a field that goes away from its vacuum value, that passes through 0. Once again, that takes a lot of energy, so it occupies as little space as possible. But now, that space isn’t a giant wall. Instead, it’s a squiggly line: a cosmic string.

Cosmic strings don’t have as dramatic a gravitational effect as domain walls. That means they might not be super-rare. There might be some we haven’t seen yet. And if we do see them, it could be because they wiggle space and time, making gravitational waves.

Cosmic strings don’t require string theory, they come from a much more basic gadget, scalar fields. We know there is one quite important scalar field, the Higgs field. The Higgs vacuum values aren’t like +1 and -1, or like the unit circle, though, so the Higgs by itself won’t make domain walls or cosmic strings. But there are a lot of proposals for scalar fields, things we haven’t discovered but that physicists think might answer lingering questions in particle physics, and some of those could have the right kind of vacuum values to give us cosmic strings. Thus, if we manage to detect cosmic strings, we could learn something about one of those lingering questions.

At Geometries and Special Functions for Physics and Mathematics in Bonn

What Might Lie Beyond, and Why

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As the new year approaches, people think about the future. Me, I’m thinking about the future of fundamental physics, about what might lie beyond the Standard Model. Physicists search for many different things, with many different motivations. Some are clear missing pieces, places where the Standard Model fails and we know we’ll need to modify it. Others are based on experience, with no guarantees but an expectation that, whatever we find, it will be surprising. Finally, some are cool possibilities, ideas that would explain something or fill in a missing piece but aren’t strictly necessary.

The Almost-Sure Things

Science isn’t math, so nothing here is really a sure thing. We might yet discover a flaw in important principles like quantum mechanics and special relativity, and it might be that an experimental result we trust turns out to be flawed. But if we chose to trust those principles, and our best experiments, then these are places we know the Standard Model is incomplete:

Neutrino Masses: The original Standard Model’s neutrinos were massless. Eventually, physicists discovered this was wrong: neutrinos oscillate, switching between different types in a way they only could if they had different masses. This result is familiar enough that some think of it as already part of the Standard Model, not really beyond. But the masses of neutrinos involve unsolved mysteries: we don’t know what those masses are, but more, there are different ways neutrinos could have mass, and we don’t yet know which is present in nature. Neutrino masses also imply the existence of an undiscovered “sterile” neutrino, a particle that doesn’t interact with the strong, weak, or electromagnetic forces.
Dark Matter Phenomena (and possibly Dark Energy Phenomena): Astronomers first suggested dark matter when they observed galaxies moving at speeds inconsistent with the mass of their stars. Now, they have observed evidence for it in a wide variety of situations, evidence which seems decisively incompatible with ordinary gravity and ordinary matter. Some solve this by introducing dark matter, others by modifying gravity, but this is more of a technical difference than it sounds: in order to modify gravity, one must introduce new quantum fields, much the same way one does when introducing dark matter. The only debate is how “matter-like” those fields need to be, but either approach goes beyond the Standard Model.
Quantum Gravity: It isn’t as hard to unite quantum mechanics and gravity as you might think. Physicists have known for decades how to write down a naive theory of quantum gravity, one that follows the same steps one might use to derive the quantum theory of electricity and magnetism. The problem is, this theory is incomplete. It works at low energies, but as the energy increases it loses the ability to make predictions, eventually giving nonsensical answers like probabilities greater than one. We have candidate solutions to this problem, like string theory, but we might not know for a long time which solution is right.
Landau Poles: Here’s a more obscure one. In particle physics we can zoom in and out in our theories, using similar theories at different scales. What changes are the coupling constants, numbers that determine the strength of the different forces. You can think of this in a loosely reductionist way, with the theories at smaller scales determining the constants for theories at larger scales. This gives workable theories most of the time, but it fails for at least one part of the Standard Model. In electricity and magnetism, the coupling constant increases as you zoom in. Eventually, it becomes infinite, and what’s more, does so at a finite energy scale. It’s still not clear how we should think about this, but luckily we won’t have to very soon: this energy scale is vastly vastly higher than even the scale of quantum gravity.
Some Surprises Guarantee Others: The Standard Model is special in a way that gravity isn’t. Even if you dial up the energy, a Standard Model calculation will always “make sense”: you never get probabilities greater than one. This isn’t true for potential deviations from the Standard Model. If the Higgs boson turns out to interact differently than we expect, it wouldn’t just be a violation of the Standard Model on its own: it would guarantee mathematically that, at some higher energy, we’d have to find something new. That was precisely the kind of argument the LHC used to find the Higgs boson: without the Higgs, something new was guaranteed to happen within the energy range of the LHC to prevent impossible probability numbers.

The Argument from (Theoretical) Experience

Everything in this middle category rests on a particular sort of argument. It’s short of a guarantee, but stronger than a dream or a hunch. While the previous category was based on calculations in theories we already know how to write down, this category relies on our guesses about theories we don’t yet know how to write.

Suppose we had a deeper theory, one that could use fewer parameters to explain the many parameters of the Standard Model. For example, it might explain the Higgs mass, letting us predict it rather than just measuring it like we do now. We don’t have a theory like that yet, but what we do have are many toy model theories, theories that don’t describe the real world but do, in this case, have fewer parameters. We can observe how these theories work, and what kinds of discoveries scientists living in worlds described by them would make. By looking at this process, we can get a rough idea of what to expect, which things in our own world would be “explained” in other ways in these theories.

The Hierarchy Problem: This is also called the naturalness problem. Suppose we had a theory that explained the mass of the Higgs, one where it wasn’t just a free parameter. We don’t have such a theory for the real Higgs, but we do have many toy models with similar behavior, ones with a boson with its mass determined by something else. In these models, though, the mass of the boson is always close to the energy scale of other new particles, particles which have a role in determining its mass, or at least in postponing that determination. This was the core reason why people expected the LHC to find something besides the Higgs. Without such new particles, the large hierarchy between the mass of the Higgs and the mass of new particles becomes a mystery, one where it gets harder and harder to find a toy model with similar behavior that still predicts something like the Higgs mass.
The Strong CP Problem: The weak nuclear force does what must seem like a very weird thing, by violating parity symmetry: the laws that govern it are not the same when you flip the world in a mirror. This is also true when you flip all the charges as well, a combination called CP (charge plus parity). But while it may seem strange that the weak force violates this symmetry, physicists find it stranger that the strong force seems to obey it. Much like in the hierarchy problem, it is very hard to construct a toy model that both predicts a strong force that maintains CP (or almost maintains it) and doesn’t have new particles. The new particle in question, called the axion, is something some people also think may explain dark matter.
Matter-Antimatter Asymmetry: We don’t know the theory of quantum gravity. Even if we did, the candidate theories we have struggle to describe conditions close to the Big Bang. But while we can’t prove it, many physicists expect the quantum gravity conditions near the Big Bang to produce roughly equal amounts of matter and antimatter. Instead, matter dominates: we live in a world made almost entirely of matter, with no evidence of large antimatter areas even far out in space. This lingering mystery could be explained if some new physics was biased towards matter instead of antimatter.
Various Problems in Cosmology: Many open questions in cosmology fall in this category. The small value of the cosmological constant is mysterious for the same reasons the small value of the Higgs mass is, but at a much larger and harder to fix scale. The early universe surprises many cosmologists by its flatness and uniformity, which has led them to propose new physics. This surprise is not because such flatness and uniformity is mathematically impossible, but because it is not the behavior they would expect out of a theory of quantum gravity.

The Cool Possibilities

Some ideas for physics beyond the standard model aren’t required, either from experience or cold hard mathematics. Instead, they’re cool, and would be convenient. These ideas would explain things that look strange, or make for a simpler deeper theory, but they aren’t the only way to do so.

Grand Unified Theories: Not the same as a “theory of everything”, Grand Unified Theories unite the three “particle physics forces”: the strong nuclear force, the weak nuclear force, and electromagnetism. Under such a theory, the different parameters that determine the strengths of those forces could be predicted from one shared parameter, with the forces only seeming different at low energies. These theories often unite the different matter particles too, but they also introduce new particles and new forces. These forces would, among other things, make protons unstable, and so giant experiments have been constructed to try to detect a proton decaying into other particles. So far none has been seen.
Low-Energy Supersymmetry: String theory requires supersymmetry, a relationship where matter and force particles share many properties. That supersymmetry has to be “broken”, which means that while the matter and force particles have the same charges, they can have wildly different masses, so that the partner particles are all still undiscovered. Those masses may be extremely high, all the way up at the scale of quantum gravity, but they could also be low enough to test at the LHC. Physicists hoped to detect such particles, as they could have been a good solution to the hierarchy problem. Now that the LHC hasn’t found these supersymmetric particles, it is much harder to solve the problem this way, though some people are still working on it.
Large Extra Dimensions: String theory also involves extra dimensions, beyond our usual three space and one time. Those dimensions are by default very small, but some proposals have them substantially bigger, big enough that we could have seen evidence for them at the LHC. These proposals could explain why gravity is so much weaker than the other forces. Much like the previous members of this category though, no evidence for this has yet been found.

I think these categories are helpful, but experts may quibble about some of my choices. I also haven’t mentioned every possible thing that could be found beyond the Standard Model. If you’ve heard of something and want to know which category I’d put it in, let me know in the comments!

Simulated Wormholes for My Real Friends, Real Wormholes for My Simulated Friends

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Maybe you’ve recently seen a headline like this:

Actually, I’m more worried that you saw that headline before it was edited, when it looked like this:

If you’ve seen either headline, and haven’t read anything else about it, then please at least read this:

Physicists have not created an actual wormhole. They have simulated a wormhole on a quantum computer.

If you’re willing to read more, then read the rest of this post. There’s a more subtle story going on here, both about physics and about how we communicate it. And for the experts, hold on, because when I say the wormhole was a simulation I’m not making the same argument everyone else is.

[And for the mega-experts, there’s an edit later in the post where I soften that claim a bit.]

The headlines at the top of this post come from an article in Quanta Magazine. Quanta is a web-based magazine covering many fields of science. They’re read by the general public, but they aim for a higher standard than many science journalists, with stricter fact-checking and a goal of covering more challenging and obscure topics. Scientists in turn have tended to be quite happy with them: often, they cover things we feel are important but that the ordinary media isn’t able to cover. (I even wrote something for them recently.)

Last week, Quanta published an article about an experiment with Google’s Sycamore quantum computer. By arranging the quantum bits (qubits) in a particular way, they were able to observe behaviors one would expect out of a wormhole, a kind of tunnel linking different points in space and time. They published it with the second headline above, claiming that physicists had created a wormhole with a quantum computer and explaining how, using a theoretical picture called holography.

This pissed off a lot of physicists. After push-back, Quanta’s twitter account published this statement, and they added the word “Holographic” to the title.

Why were physicists pissed off?

It wasn’t because the Quanta article was wrong, per se. As far as I’m aware, all the technical claims they made are correct. Instead, it was about two things. One was the title, and the implication that physicists “really made a wormhole”. The other was the tone, the excited “breaking news” framing complete with a video comparing the experiment with the discovery of the Higgs boson. I’ll discuss each in turn:

The Title

Did physicists really create a wormhole, or did they simulate one? And why would that be at all confusing?

The story rests on a concept from the study of quantum gravity, called holography. Holography is the idea that in quantum gravity, certain gravitational systems like black holes are fully determined by what happens on a “boundary” of the system, like the event horizon of a black hole. It’s supposed to be a hologram in analogy to 3d images encoded in 2d surfaces, rather than like the hard-light constructions of science fiction.

The best-studied version of holography is something called AdS/CFT duality. AdS/CFT duality is a relationship between two different theories. One of them is a CFT, or “conformal field theory”, a type of particle physics theory with no gravity and no mass. (The first example of the duality used my favorite toy theory, N=4 super Yang-Mills.) The other one is a version of string theory in an AdS, or anti-de Sitter space, a version of space-time curved so that objects shrink as they move outward, approaching a boundary. (In the first example, this space-time had five dimensions curled up in a sphere and the rest in the anti-de Sitter shape.)

These two theories are conjectured to be “dual”. That means that, for anything that happens in one theory, you can give an alternate description using the other theory. We say the two theories “capture the same physics”, even though they appear very different: they have different numbers of dimensions of space, and only one has gravity in it.

Many physicists would claim that if two theories are dual, then they are both “equally real”. Even if one description is more familiar to us, both descriptions are equally valid. Many philosophers are skeptical, but honestly I think the physicists are right about this one. Philosophers try to figure out which things are real or not real, to make a list of real things and explain everything else as made up of those in some way. I think that whole project is misguided, that it’s clarifying how we happen to talk rather than the nature of reality. In my mind, dualities are some of the clearest evidence that this project doesn’t make any sense: two descriptions can look very different, but in a quite meaningful sense be totally indistinguishable.

That’s the sense in which Quanta and Google and the string theorists they’re collaborating with claim that physicists have created a wormhole. They haven’t created a wormhole in our own space-time, one that, were it bigger and more stable, we could travel through. It isn’t progress towards some future where we actually travel the galaxy with wormholes. Rather, they created some quantum system, and that system’s dual description is a wormhole. That’s a crucial point to remember: even if they created a wormhole, it isn’t a wormhole for you.

If that were the end of the story, this post would still be full of warnings, but the title would be a bit different. It was going to be “Dual Wormholes for My Real Friends, Real Wormholes for My Dual Friends”. But there’s a list of caveats. Most of them arguably don’t matter, but the last was what got me to change the word “dual” to “simulated”.

The real world is not described by N=4 super Yang-Mills theory. N=4 super Yang-Mills theory was never intended to describe the real world. And while the real world may well be described by string theory, those strings are not curled up around a five-dimensional sphere with the remaining dimensions in anti-de Sitter space. We can’t create either theory in a lab either.
The Standard Model probably has a quantum gravity dual too, see this cute post by Matt Strassler. But they still wouldn’t have been able to use that to make a holographic wormhole in a lab.
Instead, they used a version of AdS/CFT with fewer dimensions. It relates a weird form of gravity in one space and one time dimension (called JT gravity), to a weird quantum mechanics theory called SYK, with an infinite number of quantum particles or qubits. This duality is a bit more conjectural than the original one, but still reasonably well-established.
Quantum computers don’t have an infinite number of qubits, so they had to use a version with a finite number: seven, to be specific. They trimmed the model down so that it would still show the wormhole-dual behavior they wanted. At this point, you might say that they’re definitely just simulating the SYK theory, using a small number of qubits to simulate the infinite number. But I think they could argue that this system, too, has a quantum gravity dual. The dual would have to be even weirder than JT gravity, and even more conjectural, but the signs of wormhole-like behavior they observed (mostly through simulations on an ordinary computer, which is still better at this kind of thing than a quantum computer) could be seen as evidence that this limited theory has its own gravity partner, with its own “real dual” wormhole.
But those seven qubits don’t just have the interactions they were programmed to have, the ones with the dual. They are physical objects in the real world, so they interact with all of the forces of the real world. That includes, though very weakly, the force of gravity.

And that’s where I think things break, and you have to call the experiment a simulation. You can argue, if you really want to, that the seven-qubit SYK theory has its own gravity dual, with its own wormhole. There are people who expect duality to be broad enough to include things like that.

But you can’t argue that the seven-qubit SYK theory, plus gravity, has its own gravity dual. Theories that already have gravity are not supposed to have gravity duals. If you pushed hard enough on any of the string theorists on that team, I’m pretty sure they’d admit that.

That is what decisively makes the experiment a simulation. It approximately behaves like a system with a dual wormhole, because you can approximately ignore gravity. But if you’re making some kind of philosophical claim, that you “really made a wormhole”, then “approximately” doesn’t cut it: if you don’t exactly have a system with a dual, then you don’t “really” have a dual wormhole: you’ve just simulated one.

Edit: mitchellporter in the comments points out something I didn’t know: that there are in fact proposals for gravity theories with gravity duals. They are in some sense even more conjectural than the series of caveats above, but at minimum my claim above, that any of the string theorists on the team would agree that the system’s gravity means it can’t have a dual, is probably false.

I think at this point, I’d soften my objection to the following:

Describing the system of qubits in the experiment as a limited version of the SYK theory is in one way or another an approximation. It approximates them as not having any interactions beyond those they programmed, it approximates them as not affected by gravity, and because it’s a quantum mechanical description it even approximates the speed of light as small. Those approximations don’t guarantee that the system doesn’t have a gravity dual. But in order for them to, then our reality, overall, would have to have a gravity dual. There would have to be a dual gravity interpretation of everything, not just the inside of Google’s quantum computer, and it would have to be exact, not just an approximation. Then the approximate SYK would be dual to an approximate wormhole, but that approximate wormhole would be an approximation of some “real” wormhole in the dual space-time.

That’s not impossible, as far as I can tell. But it piles conjecture upon conjecture upon conjecture, to the point that I don’t think anyone has explicitly committed to the whole tower of claims. If you want to believe that this experiment literally created a wormhole, you thus can, but keep in mind the largest asterisk known to mankind.

End edit.

If it weren’t for that caveat, then I would be happy to say that the physicists really created a wormhole. It would annoy some philosophers, but that’s a bonus.

But even if that were true, I wouldn’t say that in the title of the article.

The Title, Again

These days, people get news in two main ways.

Sometimes, people read full news articles. Reading that Quanta article is a good way to understand the background of the experiment, what was done and why people care about it. As I mentioned earlier, I don’t think anything said there was wrong, and they cover essentially all of the caveats you’d care about (except for that last one 😉 ).

Sometimes, though, people just see headlines. They get forwarded on social media, observed at a glance passed between friends. If you’re popular enough, then many more people will see your headline than will actually read the article. For many people, their whole understanding of certain scientific fields is formed by these glancing impressions.

Because of that, if you’re popular and news-y enough, you have to be especially careful with what you put in your headlines, especially when it implies a cool science fiction story. People will almost inevitably see them out of context, and it will impact their view of where science is headed. In this case, the headline may have given many people the impression that we’re actually making progress towards travel via wormholes.

Some of my readers might think this is ridiculous, that no-one would believe something like that. But as a kid, I did. I remember reading popular articles about wormholes, describing how you’d need energy moving in a circle, and other articles about optical physicists finding ways to bend light and make it stand still. Putting two and two together, I assumed these ideas would one day merge, allowing us to travel to distant galaxies faster than light.

If I had seen Quanta’s headline at that age, I would have taken it as confirmation. I would have believed we were well on the way to making wormholes, step by step. Even the New York Times headline, “the Smallest, Crummiest Wormhole You Can Imagine”, wouldn’t have fazed me.

(I’m not sure even the extra word “holographic” would have. People don’t know what “holographic” means in this context, and while some of them would assume it meant “fake”, others would think about the many works of science fiction, like Star Trek, where holograms can interact physically with human beings.)

Quanta has a high-brow audience, many of whom wouldn’t make this mistake. Nevertheless, I think Quanta is popular enough, and respectable enough, that they should have done better here.

At minimum, they could have used the word “simulated”. Even if they go on to argue in the article that the wormhole is real, and not just a simulation, the word in the title does no real harm. It would be a lie, but a beneficial “lie to children”, the basic stock-in-trade of science communication. I think they could have defended it to the string theorists they interviewed on those grounds.

The Tone

Honestly, I don’t think people would have been nearly so pissed off were it not for the tone of the article. There are a lot of physics bloggers who view themselves as serious-minded people, opposed to hype and publicity stunts. They view the research program aimed at simulating quantum gravity on a quantum computer as just an attempt to link a dying and un-rigorous research topic to an over-hyped and over-funded one, pompous storytelling aimed at promoting the careers of people who are already extremely successful.

These people tend to view Quanta favorably, because it covers serious-minded topics in a thorough way. And so many of them likely felt betrayed, seeing this Quanta article as a massive failure of that serious-minded-ness, falling for or even endorsing the hypiest of hype.

To those people, I’d like to politely suggest you get over yourselves.

Quanta’s goal is to cover things accurately, to represent all the facts in a way people can understand. But “how exciting something is” is not a fact.

Excitement is subjective. Just because most of the things Quanta finds exciting you also find exciting, does not mean that Quanta will find the things you find unexciting unexciting. Quanta is not on “your side” in some war against your personal notion of unexciting science, and you should never have expected it to be.

In fact, Quanta tends to find things exciting, in general. They were more excited than I was about the amplituhedron, and I’m an amplitudeologist. Part of what makes them consistently excited about the serious-minded things you appreciate them for is that they listen to scientists and get excited about the things they’re excited about. That is going to include, inevitably, things those scientists are excited about for what you think are dumb groupthinky hype reasons.

I think the way Quanta titled the piece was unfortunate, and probably did real damage. I think the philosophical claim behind the title is wrong, though for subtle and weird enough reasons that I don’t really fault anybody for ignoring them. But I don’t think the tone they took was a failure of journalistic integrity or research or anything like that. It was a matter of taste. It’s not my taste, it’s probably not yours, but we shouldn’t have expected Quanta to share our tastes in absolutely everything. That’s just not how taste works.

Machine Learning, Occam’s Razor, and Fundamental Physics

10 Replies

There’s a saying in physics, attributed to the famous genius John von Neumann: “With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.”

Say you want to model something, like some surprising data from a particle collider. You start with some free parameters: numbers in your model that aren’t decided yet. You then decide those numbers, “fixing” them based on the data you want to model. Your goal is for your model not only to match the data, but to predict something you haven’t yet measured. Then you can go out and check, and see if your model works.

The more free parameters you have in your model, the easier this can go wrong. More free parameters make it easier to fit your data, but that’s because they make it easier to fit any data. Your model ends up not just matching the physics, but matching the mistakes as well: the small errors that crop up in any experiment. A model like that may look like it’s a great fit to the data, but its predictions will almost all be wrong. It wasn’t just fit, it was overfit.

We have statistical tools that tell us when to worry about overfitting, when we should be impressed by a model and when it has too many parameters. We don’t actually use these tools correctly, but they still give us a hint of what we actually want to know, namely, whether our model will make the right predictions. In a sense, these tools form the mathematical basis for Occam’s Razor, the idea that the best explanation is often the simplest one, and Occam’s Razor is a critical part of how we do science.

So, did you know machine learning was just modeling data?

All of the much-hyped recent advances in artificial intelligence, GPT and Stable Diffusion and all those folks, at heart they’re all doing this kind of thing. They start out with a model (with a lot more than five parameters, arranged in complicated layers…), then use data to fix the free parameters. Unlike most of the models physicists use, they can’t perfectly fix these numbers: there are too many of them, so they have to approximate. They then test their model on new data, and hope it still works.

Increasingly, it does, and impressively well, so well that the average person probably doesn’t realize this is what it’s doing. When you ask one of these AIs to make an image for you, what you’re doing is asking what image the model predicts would show up captioned with your text. It’s the same sort of thing as asking an economist what their model predicts the unemployment rate will be when inflation goes up. The machine learning model is just way, way more complicated.

As a physicist, the first time I heard about this, I had von Neumann’s quote in the back of my head. Yes, these machines are dealing with a lot more data, from a much more complicated reality. They literally are trying to fit elephants, even elephants wiggling their trunks. Still, the sheer number of parameters seemed fishy here. And for a little bit things seemed even more fishy, when I learned about double descent.

Suppose you start increasing the number of parameters in your model. Initially, your model gets better and better. Your predictions have less and less error, your error descends. Eventually, though, the error increases again: you have too many parameters so you’re over-fitting, and your model is capturing accidents in your data, not reality.

In machine learning, weirdly, this is often not the end of the story. Sometimes, your prediction error rises, only to fall once more, in a double descent.

For a while, I found this deeply disturbing. The idea that you can fit your data, start overfitting, and then keep overfitting, and somehow end up safe in the end, was terrifying. The way some of the popular accounts described it, like you were just overfitting more and more and that was fine, was baffling, especially when they seemed to predict that you could keep adding parameters, keep fitting tinier and tinier fleas on the elephant’s trunk, and your predictions would never start going wrong. It would be the death of Occam’s Razor as we know it, more complicated explanations beating simpler ones off to infinity.

Luckily, that’s not what happens. And after talking to a bunch of people, I think I finally understand this enough to say something about it here.

The right way to think about double descent is as overfitting prematurely. You do still expect your error to eventually go up: your model won’t be perfect forever, at some point you will really overfit. It might take a long time, though: machine learning people are trying to model very complicated things, like human behavior, with giant piles of data, so very complicated models may often be entirely appropriate. In the meantime, due to a bad choice of model, you can accidentally overfit early. You will eventually overcome this, pushing past with more parameters into a model that works again, but for a little while you might convince yourself, wrongly, that you have nothing more to learn.

(You can even mitigate this by tweaking your setup, potentially avoiding the problem altogether.)

So Occam’s Razor still holds, but with a twist. The best model is simple enough, but no simpler. And if you’re not careful enough, you can convince yourself that a too-simple model is as complicated as you can get.

I was reminded of all this recently by some articles by Sabine Hossenfelder.

Hossenfelder is a critic of mainstream fundamental physics. The articles were her restating a point she’s made many times before, including in (at least) one of her books. She thinks the people who propose new particles and try to search for them are wasting time, and the experiments motivated by those particles are wasting money. She’s motivated by something like Occam’s Razor, the need to stick to the simplest possible model that fits the evidence. In her view, the simplest models are those in which we don’t detect any more new particles any time soon, so those are the models she thinks we should stick with.

I tend to disagree with Hossenfelder. Here, I was oddly conflicted. In some of her examples, it seemed like she had a legitimate point. Others seemed like she missed the mark entirely.

Talk to most astrophysicists, and they’ll tell you dark matter is settled science. Indeed, there is a huge amount of evidence that something exists out there in the universe that we can’t see. It distorts the way galaxies rotate, lenses light with its gravity, and wiggled the early universe in pretty much the way you’d expect matter to.

What isn’t settled is whether that “something” interacts with anything else. It has to interact with gravity, of course, but everything else is in some sense “optional”. Astroparticle physicists use satellites to search for clues that dark matter has some other interactions: perhaps it is unstable, sometimes releasing tiny signals of light. If it did, it might solve other problems as well.

Hossenfelder thinks this is bunk (in part because she thinks those other problems are bunk). I kind of do too, though perhaps for a more general reason: I don’t think nature owes us an easy explanation. Dark matter isn’t obligated to solve any of our other problems, it just has to be dark matter. That seems in some sense like the simplest explanation, the one demanded by Occam’s Razor.

At the same time, I disagree with her substantially more on collider physics. At the Large Hadron Collider so far, all of the data is reasonably compatible with the Standard Model, our roughly half-century old theory of particle physics. Collider physicists search that data for subtle deviations, one of which might point to a general discrepancy, a hint of something beyond the Standard Model.

While my intuitions say that the simplest dark matter is completely dark, they don’t say that the simplest particle physics is the Standard Model. Back when the Standard Model was proposed, people might have said it was exceptionally simple because it had a property called “renormalizability”, but these days we view that as less important. Physicists like Ken Wilson and Steven Weinberg taught us to view theories as a kind of series of corrections, like a Taylor series in calculus. Each correction encodes new, rarer ways that particles can interact. A renormalizable theory is just the first term in this series. The higher terms might be zero, but they might not. We even know that some terms cannot be zero, because gravity is not renormalizable.

The two cases on the surface don’t seem that different. Dark matter might have zero interactions besides gravity, but it might have other interactions. The Standard Model might have zero corrections, but it might have nonzero corrections. But for some reason, my intuition treats the two differently: I would find it completely reasonable for dark matter to have no extra interactions, but very strange for the Standard Model to have no corrections.

I think part of where my intuition comes from here is my experience with other theories.

One example is a toy model called sine-Gordon theory. In sine-Gordon theory, this Taylor series of corrections is a very familiar Taylor series: the sine function! If you go correction by correction, you’ll see new interactions and more new interactions. But if you actually add them all up, something surprising happens. Sine-Gordon turns out to be a special theory, one with “no particle production”: unlike in normal particle physics, in sine-Gordon particles can neither be created nor destroyed. You would never know this if you did not add up all of the corrections.

String theory itself is another example. In string theory, elementary particles are replaced by strings, but you can think of that stringy behavior as a series of corrections on top of ordinary particles. Once again, you can try adding these things up correction by correction, but once again the “magic” doesn’t happen until the end. Only in the full series does string theory “do its thing”, and fix some of the big problems of quantum gravity.

If the real world really is a theory like this, then I think we have to worry about something like double descent.

Remember, double descent happens when our models can prematurely get worse before getting better. This can happen if the real thing we’re trying to model is very different from the model we’re using, like the example in this explainer that tries to use straight lines to match a curve. If we think a model is simpler because it puts fewer corrections on top of the Standard Model, then we may end up rejecting a reality with infinite corrections, a Taylor series that happens to add up to something quite nice. Occam’s Razor stops helping us if we can’t tell which models are really the simple ones.

The problem here is that every notion of “simple” we can appeal to here is aesthetic, a choice based on what makes the math look nicer. Other sciences don’t have this problem. When a biologist or a chemist wants to look for the simplest model, they look for a model with fewer organisms, fewer reactions…in the end, fewer atoms and molecules, fewer of the building-blocks given to those fields by physics. Fundamental physics can’t do this: we build our theories up from mathematics, and mathematics only demands that we be consistent. We can call theories simpler because we can write them in a simple way (but we could write them in a different way too). Or we can call them simpler because they look more like toy models we’ve worked with before (but those toy models are just a tiny sample of all the theories that are possible). We don’t have a standard of simplicity that is actually reliable.

From the Wikipedia page for dark matter halos

There is one other way out of this pickle. A theory that is easier to write down is under no obligation to be true. But it is more likely to be useful. Even if the real world is ultimately described by some giant pile of mathematical parameters, if a simple theory is good enough for the engineers then it’s a better theory to aim for: a useful theory that makes peoples’ lives better.

I kind of get the feeling Hossenfelder would make this objection. I’ve seen her argue on twitter that scientists should always be able to say what their research is good for, and her Guardian article has this suggestive sentence: “However, we do not know that dark matter is indeed made of particles; and even if it is, to explain astrophysical observations one does not need to know details of the particles’ behaviour.”

Ok yes, to explain astrophysical observations one doesn’t need to know the details of dark matter particles’ behavior. But taking a step back, one doesn’t actually need to explain astrophysical observations at all.

Astrophysics and particle physics are not engineering problems. Nobody out there is trying to steer a spacecraft all the way across a galaxy, navigating the distribution of dark matter, or creating new universes and trying to make sure they go just right. Even if we might do these things some day, it will be so far in the future that our attempts to understand them won’t just be quaint: they will likely be actively damaging, confusing old research in dead languages that the field will be better off ignoring to start from scratch.

Because of that, usefulness is also not a meaningful guide. It cannot tell you which theories are more simple, which to favor with Occam’s Razor.

Hossenfelder’s highest-profile recent work falls afoul of one or the other of her principles. Her work on the foundations of quantum mechanics could genuinely be useful, but there’s no reason aside from claims of philosophical beauty to expect it to be true. Her work on modeling dark matter is at least directly motivated by data, but is guaranteed to not be useful.

I’m not pointing this out to call Hossenfelder a hypocrite, as some sort of ad hominem or tu quoque. I’m pointing this out because I don’t think it’s possible to do fundamental physics today without falling afoul of these principles. If you want to hold out hope that your work is useful, you don’t have a great reason besides a love of pretty math: otherwise, anything useful would have been discovered long ago. If you just try to model existing data as best you can, then you’re making a model for events far away or locked in high-energy particle colliders, a model no-one else besides other physicists will ever use.

I don’t know the way through this. I think if you need to take Occam’s Razor seriously, to build on the same foundations that work in every other scientific field…then you should stop doing fundamental physics. You won’t be able to make it work. If you still need to do it, if you can’t give up the sub-field, then you should justify it on building capabilities, on the kind of “practice” Hossenfelder also dismisses in her Guardian piece.

We don’t have a solid foundation, a reliable notion of what is simple and what isn’t. We have guesses and personal opinions. And until some experiment uncovers some blinding flash of new useful meaningful magic…I don’t think we can do any better than that.

Jumpstarting Elliptic Bootstrapping

4 gravitons

The trials and tribulations of four gravitons and a physicist