Book Review: We Have No Idea

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I have no idea how I’m going to review this book.

Ok fine, I have some idea.

Jorge Cham writes Piled Higher and Deeper, a webcomic with possibly the most accurate depiction of grad school available. Daniel Whiteson is a professor at the University of California, Irvine, and a member of the ATLAS collaboration (one of the two big groups that make measurements at the Large Hadron Collider). Together, they’ve written a popular science book covering everything we don’t know about fundamental physics.

Writing a book about what we don’t know is an unusual choice, and there was a real risk it would end up as just a superficial gimmick. The pie chart on the cover presents the most famous “things physicists don’t know”, dark matter and dark energy. If they had just stuck to those this would have been a pretty ordinary popular physics book.

Refreshingly, they don’t do that. After blazing through dark matter and dark energy in the first three chapters, the rest of the book focuses on a variety of other scientific mysteries.

The book contains a mix of problems that get serious research attention (matter-antimatter asymmetry, high-energy cosmic rays) and more blue-sky “what if” questions (does matter have to be made out of particles?). As a theorist, I’m not sure that all of these questions are actually mysterious (we do have some explanation of the weird “1/3” charges of quarks, and I’d like to think we understand why mass includes binding energy), but even in these cases what we really know is that they follow from “sensible assumptions”, and one could just as easily ask “what if” about those assumptions instead. Overall, these “what if” questions make the book unique, and it would be a much weaker book without them.

“We Have No Idea” is strongest when the authors actually have some idea, i.e. when Whiteson is discussing experimental particle physics. It gets weaker on other topics, where the authors seem to rely more on others’ popular treatments (their discussion of “pixels of space-time” motivated me to write this post). Still, they at least seem to have asked the right people, and their accounts are on the more accurate end of typical pop science. (Closer to Quanta than IFLScience.)

The book’s humor really ties it together, often in surprisingly subtle ways. Each chapter has its own running joke, initially a throwaway line that grows into metaphors for everything the chapter discusses. It’s a great way to help the audience visualize without introducing too many new concepts at once. If there’s one thing cartoonists can teach science communicators, it’s the value of repetition.

I liked “We Have No Idea”. It could have been more daring, or more thorough, but it was still charming and honest and fun. If you’re looking for a Christmas present to explain physics to your relatives, you won’t go wrong with this book.

Pan Narrans Scientificus

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As scientists, we want to describe the world as objectively as possible. We try to focus on what we can establish conclusively, to leave out excessive speculation and stick to cold, hard facts.

Then we have to write application letters.

Stick to the raw, un-embellished facts, and an application letter would just be a list: these papers in these journals, these talks and awards. Though we may sometimes wish applications worked that way, we don’t live in that kind of world. To apply for a job or a grant, we can’t just stick to the most easily measured facts. We have to tell a story.

The author Terry Pratchett called humans Pan Narrans, the Storytelling Ape. Stories aren’t just for fun, they’re how we see the world, how we organize our perceptions and actions. Without a story, the world doesn’t make sense. And that applies even to scientists.

Applications work best when they tell a story: how did you get here, and where are you going? Scientific papers, similarly, require some sort of narrative: what did you do, and why did you do it? When teaching or writing about science, we almost never just present the facts. We try to fit it into a story, one that presents the facts but also makes sense, in that deliciously human way. A story, more than mere facts, lets us project to the future, anticipating what you’ll do with that grant money or how others will take your research in new directions.

It’s important to remember, though, that stories aren’t actually facts. You can’t get too attached to one story, you have to be willing to shift as new facts come in. Those facts can be scientific measurements, but they can also be steps in your career. You aren’t going to tell the same story when applying to grad school as when you’re trying for tenure, and that’s not just because you’ll have more to tell. The facts of your life will be organized in new ways, rearranging in importance as the story shifts.

Keep your stories in mind as you write or do science. Think about your narrative, the story you’re using to understand the world. Think about what it predicts, how the next step in the story should go. And be ready to start a new story when you need to.

How to Get a “Minimum Scale” Without Pixels

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

My Other Brain (And My Other Other Brain)

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What does a theoretical physicist do all day? We sit and think.

Most of us can’t do all that thinking in our heads, though. Maybe Steven Hawking could, but the rest of us need to visualize what we’re thinking. Our memories, too, are all-too finite, prone to forget what we’re doing midway through a calculation.

So rather than just use our imagination and memory, we use another imagination, another memory: a piece of paper. Writing is the simplest “other brain” we have access to, but even by itself it’s a big improvement, adding weeks of memory and the ability to “see” long calculations at work.

But even augmented by writing, our brains are limited. We can only calculate so fast. What’s more, we get bored: doing the same thing mechanically over and over is not something our brains like to do.

Luckily, in the modern era we have access to other brains: computers.

As I write, the “other brain” sitting on my desk works out a long calculation. Using programs like Mathematica or Maple, or more serious programming languages, I can tell my “other brain” to do something and it will do it, quickly and without getting bored.

My “other brain” is limited too. It has only so much memory, only so much speed, it can only do so many calculations at once. While it’s thinking, though, I can find yet another brain to think at the same time. Sometimes that’s just my desktop, sitting back in my office in Denmark. Sometimes I have access to clusters, blobs of synchronized brains to do my bidding.

While I’m writing this, my “brains” are doing five different calculations (not counting any my “real brain” might be doing). I’m sitting and thinking, as a theoretical physicist should.

Why the Coupling Constants Aren’t Constant: Epistemology and Pragmatism

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If you’ve heard a bit about physics, you might have heard that each of the fundamental forces (electromagnetism, the weak nuclear force, the strong nuclear force, and gravity) has a coupling constant, a number, handed down from nature itself, that determines how strong of a force it is. Maybe you’ve seen them in a table, like this:

tablefromhyperphysics

If you’ve heard a bit more about physics, though, you’ll have heard that those coupling constants aren’t actually constant! Instead, they vary with energy. Maybe you’ve seen them plotted like this:

phypub4highen

The usual way physicists explain this is in terms of quantum effects. We talk about “virtual particles”, and explain that any time particles and forces interact, these virtual particles can pop up, adding corrections that change with the energy of the interacting particles. The coupling constant includes all of these corrections, so it can’t be constant, it has to vary with energy.

renormalized-vertex

Maybe you’re happy with this explanation. But maybe you object:

“Isn’t there still a constant, though? If you ignore all the virtual particles, and drop all the corrections, isn’t there some constant number you’re correcting? Some sort of `bare coupling constant’ you could put into a nice table for me?”

There are two reasons I can’t do that. One is an epistemological reason, that comes from what we can and cannot know. The other is practical: even if I knew the bare coupling, most of the time I wouldn’t want to use it.

Let’s start with the epistemology:

The first thing to understand is that we can’t measure the bare coupling directly. When we measure the strength of forces, we’re always measuring the result of quantum corrections. We can’t “turn off” the virtual particles.

You could imagine measuring it indirectly, though. You’d measure the end result of all the corrections, then go back and calculate. That calculation would tell you how big the corrections were supposed to be, and you could subtract them off, solve the equation, and find the bare coupling.

And this would be a totally reasonable thing to do, except that when you go and try to calculate the quantum corrections, instead of something sensible, you get infinity.

We think that “infinity” is due to our ignorance: we know some of the quantum corrections, but not all of them, because we don’t have a final theory of nature. In order to calculate anything we need to hedge around that ignorance, with a trick called renormalization. I talk about that more in an older post. The key message to take away there is that in order to calculate anything we need to give up the hope of measuring certain bare constants, even “indirectly”. Once we fix a few constants that way, the rest of the theory gives reliable predictions.

So we can’t measure bare constants, and we can’t reason our way to them. We have to find the full coupling, with all the quantum corrections, and use that as our coupling constant.

Still, you might wonder, why does the coupling constant have to vary? Can’t I just pick one measurement, at one energy, and call that the constant?

This is where pragmatism comes in. You could fix your constant at some arbitrary energy, sure. But you’ll regret it.

In particle physics, we usually calculate in something called perturbation theory. Instead of calculating something exactly, we have to use approximations. We add up the approximations, order by order, expecting that each time the corrections will get smaller and smaller, so we get closer and closer to the truth.

And this works reasonably well if your coupling constant is small enough, provided it’s at the right energy.

If your coupling constant is at the wrong energy, then your quantum corrections will notice the difference. They won’t just be small numbers anymore. Instead, they end up containing logarithms of the ratio of energies. The more difference between your arbitrary energy scale and the correct one, the bigger these logarithms get.

This doesn’t make your calculation wrong, exactly. It makes your error estimate wrong. It means that your assumption that the next order is “small enough” isn’t actually true. You’d need to go to higher and higher orders to get a “good enough” answer, if you can get there at all.

Because of that, you don’t want to think about the coupling constants as actually constant. If we knew the final theory then maybe we’d know the true numbers, the ultimate bare coupling constants. But we still would want to use coupling constants that vary with energy for practical calculations. We’d still prefer the plot, and not just the table.

Amplitudes in the LHC Era at GGI

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I’m at the Galileo Galilei Institute in Florence this week, for a program on Amplitudes in the LHC Era.

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I didn’t notice this ceiling decoration last time I was here. These guys really love their Galileo stuff.

I’ll be here for three weeks of the full six-week program, hopefully plenty of time for some solid collaboration. This week was the “conference part”, with a flurry of talks over three days.

I missed the first day, which focused on the “actually useful” side of scattering amplitudes, practical techniques that can be applied to real Standard Model calculations. Luckily the slides are online, and at least some of the speakers are still around to answer questions. I’m particularly curious about Daniel Hulme’s talk, about an approximation strategy I hadn’t heard of before.

The topics of the next two days were more familiar, but the talks still gave me a better appreciation for the big picture behind them. From Johannes Henn’s thoughts about isolating a “conformal part” of general scattering amplitudes to Enrico Herrmann’s roadmap for finding an amplituhedron for supergravity, people seem to be aiming for bigger goals than just the next technical hurdle. It will be nice to settle in over the next couple weeks and get a feeling for what folks are working on next.

Cosmology, or Cosmic Horror?

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Around Halloween, I have a tradition of posting about the “spooky” side of physics. This year, I’ll be comparing two no doubt often confused topics, Cosmic Horror and Cosmology.

cthulhu_and_r27lyeh

Pro tip: if this guy shows up, it’s probably Cosmic Horror

Cosmic Horror

Cosmology
Started in the 1920’s with the work of Howard Phillips Lovecraft Started in the 1920’s with the work of Alexander Friedmann
Unimaginably ancient universe Precisely imagined ancient universe
In strange ages even death may die Strange ages, what redshift is that?
An expedition to Antarctica uncovers ruins of a terrifying alien civilization An expedition to Antarctica uncovers…actually, never mind, just dust
Alien beings may propagate in hidden dimensions Gravitons may propagate in hidden dimensions
Cultists compete to be last to be eaten by the Elder Gods Grad students compete to be last to realize there are no jobs
Oceanic “deep ones” breed with humans Have you seen daycare costs in a university town? No way.
Variety of inventive and bizarre creatures, inspiring libraries worth of copycat works Fritz Zwicky
Hollywood adaptations are increasingly popular, not very faithful to source material Actually this is exactly the same
Can waste hours on an ultimately fruitless game of Arkham Horror Can waste hours on an ultimately fruitless argument with Paul Steinhardt
No matter what we do, eventually Azathoth will kill us all No matter what we do, eventually vacuum decay will kill us all

A Micrographia of Beastly Feynman Diagrams

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Earlier this year, I had a paper about the weird multi-dimensional curves you get when you try to compute trickier and trickier Feynman diagrams. These curves were “Calabi-Yau”, a type of curve string theorists have studied as a way to curl up extra dimensions to preserve something called supersymmetry. At the time, string theorists asked me why Calabi-Yau curves showed up in these Feynman diagrams. Do they also have something to do with supersymmetry?

I still don’t know the general answer. I don’t know if all Feynman diagrams have Calabi-Yau curves hidden in them, or if only some do. But for a specific class of diagrams, I now know the reason. In this week’s paper, with Jacob Bourjaily, Andrew McLeod, and Matthias Wilhelm, we prove it.

We just needed to look at some more exotic beasts to figure it out.

tardigrade_eyeofscience_960

Like this guy!

Meet the tardigrade. In biology, they’re incredibly tenacious microscopic animals, able to withstand the most extreme of temperatures and the radiation of outer space. In physics, we’re using their name for a class of Feynman diagrams.

even_loop_tardigrades

A clear resemblance!

There is a long history of physicists using whimsical animal names for Feynman diagrams, from the penguin to the seagull (no relation). We chose to stick with microscopic organisms: in addition to the tardigrades, we have paramecia and amoebas, even a rogue coccolithophore.

The diagrams we look at have one thing in common, which is key to our proof: the number of lines on the inside of the diagram (“propagators”, which represent “virtual particles”) is related to the number of “loops” in the diagram, as well as the dimension. When these three numbers are related in the right way, it becomes relatively simple to show that any curves we find when computing the Feynman diagram have to be Calabi-Yau.

This includes the most well-known case of Calabi-Yaus showing up in Feynman diagrams, in so-called “banana” or “sunrise” graphs. It’s closely related to some of the cases examined by mathematicians, and our argument ended up pretty close to one made back in 2009 by the mathematician Francis Brown for a different class of diagrams. Oddly enough, neither argument works for the “traintrack” diagrams from our last paper. The tardigrades, paramecia, and amoebas are “more beastly” than those traintracks: their Calabi-Yau curves have more dimensions. In fact, we can show they have the most dimensions possible at each loop, provided all of our particles are massless. In some sense, tardigrades are “as beastly as you can get”.

We still don’t know whether all Feynman diagrams have Calabi-Yau curves, or just these. We’re not even sure how much it matters: it could be that the Calabi-Yau property is a red herring here, noticed because it’s interesting to string theorists but not so informative for us. We don’t understand Calabi-Yaus all that well yet ourselves, so we’ve been looking around at textbooks to try to figure out what people know. One of those textbooks was our inspiration for the “bestiary” in our title, an author whose whimsy we heartily approve of.

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Like the classical bestiary, we hope that ours conveys a wholesome moral. There are much stranger beasts in the world of Feynman diagrams than anyone suspected.

The Amplitudes Assembly Line

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In the amplitudes field, we calculate probabilities for particles to interact.

We’re trying to improve on the old-school way of doing this, a kind of standard assembly line. First, you define your theory, writing down something called a Lagrangian. Then you start drawing Feynman diagrams, starting with the simplest “tree” diagrams and moving on to more complicated “loops”. Using rules derived from your Lagrangian, you translate these Feynman diagrams into a set of integrals. Do the integrals, and finally you have your answer.

Our field is a big tent, with many different approaches. Despite that, a kind of standard picture has emerged. It’s not the best we can do, and it’s certainly not what everyone is doing. But it’s in the back of our minds, a default to compare against and improve on. It’s the amplitudes assembly line: an “industrial” process that takes raw assumptions and builds particle physics probabilities.

amplitudesassembly

  1. Start with some simple assumptions about your particles (what mass do they have? what is their spin?) and your theory (minimally, it should obey special relativity). Using that, find the simplest “trees”, involving only three particles: one particle splitting into two, or two particles merging into one.
  2. With the three-particle trees, you can now build up trees with any number of particles, using a technique called BCFW (named after its inventors, Ruth Britto, Freddy Cachazo, Bo Feng, and Edward Witten).
  3. Now that you’ve got trees with any number of particles, it’s time to get loops! As it turns out, you can stitch together your trees into loops, using a technique called generalized unitarity. To do this, you have to know what kinds of integrals are allowed to show up in your result, and a fair amount of effort in the field goes into figuring out a better “basis” of integrals.
  4. (Optional) Generalized unitarity will tell you which integrals you need to do, but those integrals may be related to each other. By understanding where these relations come from, you can reduce to a basis of fewer “master” integrals. You can also try to aim for integrals with particular special properties, quite a lot of effort goes in to improving this basis as well. The end goal is to make the final step as easy as possible:
  5. Do the integrals! If you just want to get a number out, you can use numerical methods. Otherwise, there’s a wide variety of choices available. Methods that use differential equations are probably the most popular right now, but I’m a fan of other options.

Some people work to improve one step in this process, making it as efficient as possible. Others skip one step, or all of them, replacing them with deeper ideas. Either way, the amplitudes assembly line is the background: our current industrial machine, churning out predictions.

Congratulations to Arthur Ashkin, Gérard Mourou, and Donna Strickland!

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The 2018 Physics Nobel Prize was announced this week, awarded to Arthur Ashkin, Gérard Mourou, and Donna Strickland for their work in laser physics.

nobel2018Some Nobel prizes recognize discoveries of the fundamental nature of reality. Others recognize the tools that make those discoveries possible.

Ashkin developed techniques that use lasers to hold small objects in place, culminating in “optical tweezers” that can pick up and move individual bacteria. Mourou and Strickland developed chirped pulse amplification, the current state of the art in extremely high-power lasers. Strickland is only the third woman to win the Nobel prize in physics, Ashkin at 96 is the oldest person to ever win the prize.

(As an aside, the phrase “optical tweezers” probably has you imagining two beams of laser light pinching a bacterium between them, like microscopic lightsabers. In fact, optical tweezers use a single beam, focused and bent so that if an object falls out of place it will gently roll back to the middle of the beam. Instead of tweezers, it’s really more like a tiny laser spoon.)

The Nobel announcement emphasizes practical applications, like eye surgery. It’s important to remember that these are research tools as well. I wouldn’t have recognized the names of Ashkin, Mourou, and Strickland, but I recognized atom trapping, optical tweezers, and ultrashort pulses. Hang around atomic physicists, or quantum computing experiments, and these words pop up again and again. These are essential tools that have given rise to whole subfields. LIGO won a Nobel based on the expectation that it would kick-start a vast new area of research. Ashkin, Mourou, and Strickland’s work already has.