Tag Archives: particle physics

Stories Backwards and Forwards

You can always start with “once upon a time”…

I come up with tricks to make calculations in particle physics easier. That’s my one-sentence story, or my most common one. If I want to tell a longer story, I have more options.

Here’s one longer story:

I want to figure out what Nature is telling us. I want to take all the data we have access to that has anything to say about fundamental physics, every collider and gravitational wave telescope and ripple in the overall structure of the universe, and squeeze it as hard as I can until something comes out. I want to make sure we understand the implications of our current best theories as well as we can, to as high precision as we can, because I want to know whether they match what we see.

To do that, I am starting with a type of calculation I know how to do best. That’s both because I can make progress with it, and because it will be important for making these inferences, for testing our theories. I am following a hint in a theory that definitely does not describe the real world, one that is both simpler to work with and surprisingly complex, one that has a good track record, both for me and others, for advancing these calculations. And at the end of the day, I’ll make our ability to infer things from Nature that much better.

Here’s another:

Physicists, unknowing, proposed a kind of toy model, one often simpler to work with but not necessarily simpler to describe. Using this model, they pursued increasingly elaborate calculations, and time and time again, those calculations surprised them. The results were not random, not a disorderly mess of everything they could plausibly have gotten. Instead, they had structure, symmetries and patterns and mathematical properties that the physicists can’t seem to explain. If we can explain them, we will advance our knowledge of models and theories and ideas, geometry and combinatorics, learning more about the unexpected consequences of the rules we invent.

We can also help the physicists advance physics, of course. That’s a happy accident, but one that justifies the money and time, showing the rest of the world that understanding consequences of rules is still important and valuable.

These seem like very different stories, but they’re not so different. They change in order, physics then math or math then physics, backwards and forwards. By doing that, they change in emphasis, in where they’re putting glory and how they’re catching your attention. But at the end of the day, I’m investigating mathematical mysteries, and I’m advancing our ability to do precision physics.

(Maybe you think that my motivation must lie with one of these stories and not the other. One is “what I’m really doing”, the other is a lie made up for grant agencies.
Increasingly, I don’t think people work like that. If we are at heart stories, we’re retroactive stories. Our motivation day to day doesn’t follow one neat story or another. We move forward, we maybe have deep values underneath, but our accounts of “why” can and will change depending on context. We’re human, and thus as messy as that word should entail.)

I can tell more than two stories if I want to. I won’t here. But this is largely what I’m working on at the moment. In applying for grants, I need to get the details right, to sprinkle the right references and the right scientific arguments, but the broad story is equally important. I keep shuffling that story, a pile of not-quite-literal index cards, finding different orders and seeing how they sound, imagining my audience and thinking about what stories would work for them.

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.

It’s Only a Model

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Last week, I said that the current best estimate for the age of the universe, 13.8 billion years old, is based on a mathematical model. In order to get that number, astronomers had to assume the universe evolved in a particular way, according to a model where the universe is composed of ordinary matter, dark matter, and dark energy. In other words, the age of the universe is a model-dependent statement.

Reading that, you might ask whether we can do better. What about a model-independent measurement of the age of the universe?

As intuitive as it might seem, we can’t actually do that. In fact, if we’re really strict about it, we can’t get a model-independent measurement of anything at all. Everything is based on a model.

Imagine stepping on your bathroom scale, getting a mass in kilograms. The number it gives you seems as objective as anything. But to get that number, you have to trust that a number of models are true. You have to model gravity, to assume that the scale’s measurement of your weight gives you the right mass based on the Earth’s surface gravity being approximately constant. You have to model the circuits and sensors in the scale, and be confident that you understand how they’re supposed to work. You have to model people: to assume that the company that made the scale tested it accurately, and that the people who sold it to you didn’t lie about where it came from. And finally, you have to model error: you know that the scale can’t possibly give you your exact weight, so you need a rough idea of just how far off it can reasonably be.

Everything we know is like this. Every measurement in science builds on past science, on our understanding of our measuring equipment and our trust in others. Everything in our daily lives comes through a network of assumptions about the world around us. Everything we perceive is filtered through instincts, our understanding of our own senses and knowledge of when they do and don’t trick us.

Ok, but when I say that the age of the universe is model-dependent, I don’t really mean it like that, right?

Everything we know is model-dependent, but only some model-dependence is worth worrying about. Your knowledge of your bathroom scale comes from centuries-old physics of gravity, widely-applied principles of electronics, and a trust in the function of basic products that serves you well in every other aspect of your life. The models that knowledge depends on aren’t really in question, especially not when you just want to measure your weight.

Some measurements we make in physics are like this too. When the experimental collaborations at the LHC measured the Higgs mass, they were doing something far from routine. But the models they based that measurement on, models of particle physics and particle detector electronics and their own computer code, are still so well-tested that it mostly doesn’t make sense to think of this as a model-dependent measurement. If we’re questioning the Higgs mass, it’s only because we’re questioning something much bigger.

The age of the universe, though, is trickier. Our most precise measurements are based on a specific model: we estimate what the universe is made of and how fast it’s expanding, plug it into our model of how the universe changes over time, and get an estimate for the age. You might suggest that we should just look out into the universe and find the oldest star, but that’s model-dependent too. Stars don’t have rings like trees. Instead, to estimate the age of a star we have to have some model for what kind of light it emits, and for how that light has changed over the history of the universe before it reached us.

These models are not quite as well-established as the models behind particle physics, let alone those behind your bathroom scale. Our models of stars are pretty good, applied to many types of stars in many different galaxies, but they do involve big, complicated systems involving many types of extreme and difficult to estimate physics. Star models get revised all the time, usually in minor ways but occasionally in more dramatic ones. Meanwhile, our model of the whole universe is powerful, but by its very nature much less-tested. We can test it on observations of the whole universe today, or on observations of the whole universe in the past (like the cosmic microwave background). And it works well for these, better than any other model. But it’s not inconceivable, not unrealistic, and above all not out of context, that another model could take its place. And if it did, many of the model-dependent measurements we’ve based on it will have to change.

So that’s why, while everything we know is model-dependent, some are model-dependent in a more important way. Some things, even if we feel they have solid backing, may well turn out to be wrong, in a way that we have reason to take seriously. The age of the universe is pretty well-established as these things go, but it still is one of those types of things, where there is enough doubt in our model that we can’t just take the measurement at face value.

Not Made of Photons Either

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If you know a bit about quantum physics, you might have heard that everything is made out of particles. Mass comes from Higgs particles, gravity from graviton particles, and light and electricity and magnetism from photon particles. The particles are the “quanta”, the smallest possible units of stuff.

This is not really how quantum physics works.

You might have heard (instead, or in addition), that light is both particle and wave. Maybe you’ve heard it said that it is both at the same time, or that it is one or the other, depending on how you look at it.

This is also not really how quantum physics works.

If you think that light is both a particle and a wave, you might get the impression there are only two options. This is better than thinking there is only one option, but still not really the truth. The truth is there are many options. It all depends on what you measure.

Suppose you have a particle collider, like the Large Hadron Collider at CERN. Sometimes, the particles you collide release photons. You surround the collision with particle detectors. When a photon hits them, these particle detectors amplify it, turning it into an electrical signal in a computer.

If you want to predict what those particle detectors see, you might put together a theory of photons. You’ll try to calculate the chance that you see some specific photon with some specific energy to some reasonable approximation…and you’ll get infinity.

You might think you’ve heard this story before. Maybe you’ve heard people talk about calculations in quantum field theory that give infinity, with buzzwords like divergences and renormalization. You may remember them saying that this is a sign that our theories are incomplete, that there are parameters we can’t predict or that the theory is just a low-energy approximation to a deeper theory.

This is not that story. That story is about “ultraviolet divergences”, infinities that come from high-energy particles. This story is about “infrared divergences” from low-energy particles. Infrared divergences don’t mean our theory is incomplete. Our theory is fine. We’re just using it wrong.

The problem is that I lied to you a little bit, earlier. I told you that your particle detectors can detect photons, so you might have imagined they can detect any photon you like. But that is impossible. A photon’s energy is determined by its wavelength: X-rays have more energy than UV light, which has more energy than IR light, which has more energy than microwaves. No matter how you build your particle detector, there will be some energy low enough that it cannot detect, a wavelength of photons that gives no response at all.

When you think you’re detecting just one photon, then, you’re not actually detecting just one photon. You’re detecting one photon, plus some huge number of undetectable photons that are too low-energy to see. We call these soft photons. You don’t know how many soft photons you generate, because you can’t detect them. Thus, as always in quantum mechanics, you have to add up every possibility.

That adding up is crucial, because it makes the infinite results go away. The different infinities pair up, negative and positive, at each order of approximation. Those pesky infrared divergences aren’t really a problem, provided you’re honest about what you’re actually detecting.

But while infrared divergences aren’t really a problem, they do say something about your model. You were modeling particles as single photons, and that made your calculations complicated, with a lot of un-physical infinite results. But you could, instead, have made another model. You could have modeled particles as dressed photons: one photon, plus a cloud of soft photons.

For a particle physicists, these dressed photons have advantages and disadvantages. They aren’t always the best tool, and can be complicated to use. But one thing they definitely do is avoid infinite results. You can interpret them a little more easily.

That ease, though, raises a question. You started out with a model in which each particle you detect was a photon. You could have imagined it as a model of reality, one in which every electromagnetic field was made up of photons.

But then you found another model, one which sometimes makes more sense. And in that model, instead, you model your particles as dressed photons. You could then once again imagine a model of reality, now with every electromagnetic field made up of dressed photons, not the ordinary ones.

So now it looks like you have three options. Are electromagnetic fields made out of waves, or particles…or dressed particles?

That’s a trick question. It was always a trick question, and will always be a trick question.

Ancient Greek philosophers argued about whether everything was made of water, or fire, or innumerable other things. Now, we teach children that science has found the answer: a world made of atoms, or protons, or quarks.

But scientists are actually answering a different, and much more important, question. “What is everything really made of?” is still a question for philosophers. We scientists want to know what we will observe. We want a model that makes predictions, that tells us what actions we can do and what results we should expect, that lets us develop technology and improve our lives.

And if we want to make those predictions, then our models can make different choices. We can arrange things in different ways, grouping the fluid possibilities of reality into different concrete “stuff”. We can choose what to measure, and how best to describe it. We don’t end up with one “what everything is made of”, but more than one, different stories for different contexts. As long as those models make the right predictions, we’ve done the only job we ever needed to do.

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.

Visiting CERN

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So, would you believe I’ve never visited CERN before?

I was at CERN for a few days this week, visiting friends and collaborators and giving an impromptu talk. Surprisingly, this is the first time I’ve been, a bit of an embarrassing admission for someone who’s ostensibly a particle physicist.

Despite that, CERN felt oddly familiar. The maze of industrial buildings and winding roads, the security gates and cards (and work-arounds for when you arrive outside of card-issuing hours, assisted by friendly security guards), the constant construction and remodeling, all of it reminded me of the times I visited SLAC during my PhD. This makes a lot of sense, of course: one accelerator is at least somewhat like another. But besides a visit to Fermilab for a conference several years ago, I haven’t been in many other places like that since then.

(One thing that might have also been true of SLAC and Fermilab but I never noticed: CERN buildings not only have evacuation instructions for the building in case of a fire, but also evacuation instructions for the whole site.)

CERN is a bit less “pretty” than SLAC on average, without the nice grassy area in the middle or the California sun that goes with it. It makes up for it with what seems like more in terms of outreach resources, including a big wooden dome of a mini-museum sponsored by Rolex, and a larger visitor center still under construction.

The outside, including a sculpture depicting the history of science with the Higgs boson discovery on the “cutting edge”

The inside. Bubbles on the ground contain either touchscreens or small objects (detectors, papers, a blackboard with the string theory genus expansion for some reason). Bubbles in the air were too high for me to check.

CERN hosts a variety of theoretical physicists doing various different types of work. I was hosted by the “QCD group”, but the string theorists just down the hall include a few people I know as well. The lounge had a few cardboard signs hidden under the table, leftovers of CERN’s famous yearly Christmas play directed by John Ellis.

It’s been a fun, if brief, visit. I’ll likely get to see a bit more this summer, when they host Amplitudes 2023. Until then, it was fun reconnecting with that “accelerator feel”.

Valentine’s Day Physics Poem 2023

Why Dark Matter Feels Like Cheating (And Why It Isn’t)

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I’ve never met someone who believed the Earth was flat. I’ve met a few who believed it was six thousand years old, but not many. Occasionally, I run into crackpots who rail against relativity or quantum mechanics, or more recent discoveries like quarks or the Higgs. But for one conclusion of modern physics, the doubters are common. For this one idea, the average person may not insist that the physicists are wrong, but they’ll usually roll their eyes a little bit, ask the occasional “really?”

That idea is dark matter.

For the average person, dark matter doesn’t sound like normal, responsible science. It sounds like cheating. Scientists try to explain the universe, using stars and planets and gravity, and eventually they notice the equations don’t work, so they just introduce some new matter nobody can detect. It’s as if a budget didn’t add up, so the accountant just introduced some “dark expenses” to hide the problem.

Part of what’s going on here is that fundamental physics, unlike other fields, doesn’t have to reduce to something else. An accountant has to explain the world in terms of transfers of money, a chemist in terms of atoms and molecules. A physicist has to explain the world in terms of math, with no more restrictions than that. Whatever the “base level” of another field is, physics can, and must, go deeper.

But that doesn’t explain everything. Physics may have to explain things in terms of math, but we shouldn’t just invent new math whenever we feel like it. Surely, we should prefer explanations in terms of things we know to explanations in terms of things we don’t know. The question then becomes, what justifies the preference? And when do we get to break it?

Imagine you’re camping in your backyard. You’ve brought a pack of jumbo marshmallows. You wake up to find a hole torn in the bag, a few marshmallows strewn on a trail into the bushes, the rest gone. You’re tempted to imagine a new species of ant, with enormous jaws capable of ripping open plastic and hauling the marshmallows away. Then you remember your brother likes marshmallows, and it’s probably his fault.

Now imagine instead you’re camping in the Amazon rainforest. Suddenly, the ant explanation makes sense. You may not have a particular species of ants in mind, but you know the rainforest is full of new species no-one has yet discovered. And you’re pretty sure your brother couldn’t have flown to your campsite in the middle of the night and stolen your marshmallows.

We do have a preference against introducing new types of “stuff”, like new species of ants or new particles. We have that preference because these new types of stuff are unlikely, based on our current knowledge. We don’t expect new species of ants in our backyards, because we think we have a pretty good idea of what kinds of ants exist, and we think a marshmallow-stealing brother is more likely. That preference gets dropped, however, based on the strength of the evidence. If it’s very unlikely our brother stole the marshmallows, and if we’re somewhere our knowledge of ants is weak, then the marshmallow-stealing ants are more likely.

Dark matter is a massive leap. It’s not a massive leap because we can’t see it, but simply because it involves new particles, particles not in our Standard Model of particle physics. (Or, for the MOND-ish fans, new fields not present in Einstein’s theory of general relativity.) It’s hard to justify physics beyond the Standard Model, and our standards for justifying it are in general very high: we need very precise experiments to conclude that the Standard Model is well and truly broken.

For dark matter, we keep those standards. The evidence for some kind of dark matter, that there is something that can’t be explained by just the Standard Model and Einstein’s gravity, is at this point very strong. Far from a vague force that appears everywhere, we can map dark matter’s location, systematically describe its effect on the motion of galaxies to clusters of galaxies to the early history of the universe. We’ve checked if there’s something we’ve left out, if black holes or unseen planets might cover it, and they can’t. It’s still possible we’ve missed something, just like it’s possible your brother flew to the Amazon to steal your marshmallows, but it’s less likely than the alternatives.

Also, much like ants in the rainforest, we don’t know every type of particle. We know there are things we’re missing: new types of neutrinos, or new particles to explain quantum gravity. These don’t have to have anything to do with dark matter, they might be totally unrelated. But they do show that we should expect, sometimes, to run into particles we don’t already know about. We shouldn’t expect that we already know all the particles.

If physicists did what the cartoons suggest, it really would be cheating. If we proposed dark matter because our equations didn’t match up, and stopped checking, we’d be no better than an accountant adding “dark money” to a budget. But we didn’t do that. When we argue that dark matter exists, it’s because we’ve actually tried to put together the evidence, because we’ve weighed it against the preference to stick with the Standard Model and found the evidence tips the scales. The instinct to call it cheating is a good instinct, one you should cultivate. But here, it’s an instinct physicists have already taken into account.

4 gravitons

Stories about physics from someone who's been there