Tag Archives: science communication

Knowing Too Little, Knowing Too Much

Pi in the Sky Science Journalism

You’ve probably seen it somewhere on your facebook feed, likely shared by a particularly wide-eyed friend: pi found hidden in the hydrogen atom!

From the headlines, this sounds like some sort of kabbalistic nonsense, like finding the golden ratio in random pictures.

Read the actual articles, and the story is a bit more reasonable. The last two I linked above seem to be decent takes on it, they’re just saddled with ridiculous headlines. As usual, I blame the editors. This time, they’ve obscured an interesting point about the link between physics and mathematics.

So what does “pi found hidden in the hydrogen atom” actually mean?

It doesn’t mean that there’s some deep importance to the number pi in nature, beyond its relevance in mathematics in general. The reason that pi is showing up here isn’t especially deep.

It isn’t trivial either, though. I’ve seen a few people whose first response to this article was “of course they found pi in the hydrogen atom, hydrogen atoms are spherical!” That’s not what’s going on here. The connection isn’t about the shape of the hydrogen atom, it’s about one particular technique for estimating its energy.

Carl Hagen is a physicist at the University of Rochester who was teaching a quantum mechanics class in which he taught a well-known approximation technique called the variational principle. Specifically, he had his students apply this technique to the hydrogen atom. The nice thing about the hydrogen atom is that it’s one of the few atoms simple enough that it’s possible to find its energy levels exactly. The exact calculation can then be compared to the approximation.

What Hagen noticed was that this approximation was surprisingly good, especially for high energy states for which it wasn’t expected to be. In the end, working with Rochester math professor Tamar Friedmann, he figured out that the variational principle was making use of a particular identity between a type of mathematical functions, called Gamma functions, that are quite common in physics. Using those Gamma functions, the two researchers were able to re-derive what turned out to be a 17th century formula for pi, giving rise to a much cleaner proof for that formula than had been known previously.

So pi isn’t appearing here because “the hydrogen atom is a sphere”. It’s appearing because pi appears all over the place in physics, and because in general, the same sorts of structures appear again and again in mathematics.

Pi’s appearance in the hydrogen atom is thus not very special, regardless. What is a little bit special is the fact that, using the hydrogen atom, these folks were able to find a cleaner proof of an old approximation for pi, one that mathematicians hadn’t found before.

That, if anything, is the interesting part of this news story, but it’s also part of a broader trend, one in which physicists provide “physics proofs” for mathematical results. One of the more famous accomplishments of string theory is a class of “physics proofs” of this sort, using a principle called mirror symmetry.

The existence of “physics proofs” doesn’t mean that mathematics is secretly constrained by the physical world. Rather, they’re a result of the fact that physicists are interested in different aspects of mathematics, and in general are a bit more reckless in using approximations that haven’t been mathematically vetted. A physicist can sometimes prove something in just a few lines that mathematicians would take many pages to prove, but usually they do this by invoking a structure that would take much longer for a mathematician to define. As physicists, we’re building on the shoulders of other physicists, using concepts that mathematicians usually don’t have much reason to bother with. That’s why it’s always interesting when we find something like the Amplituhedron, a clean mathematical concept hidden inside what would naively seem like a very messy construction. It’s also why “physics proofs” like this can happen: we’re dealing with things that mathematicians don’t naturally consider.

So please, ignore the pi-in-the-sky headlines. Some physicists found a trick, some mathematicians found it interesting, the hydrogen atom was (quite tangentially) involved…and no nonsense needs to be present.

Using Effective Language

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Physicists like to use silly names for things, but sometimes it’s best to just use an everyday word. It can trigger useful intuitions, and it makes remembering concepts easier. What gets confusing, though, is when the everyday word you use has a meaning that’s not quite the same as the colloquial one.

“Realism” is a pretty classic example, where Bell’s elegant use of the term in quantum mechanics doesn’t quite match its common usage, leading to inevitable confusion whenever it’s brought up. “Theory” is such a useful word that multiple branches of science use it…with different meanings! In both cases, the naive meaning of the word is the basis of how it gets used scientifically…just not the full story.

There are two things to be wary of here. First, those of us who communicate science must be sure to point out when a word we use doesn’t match its everyday meaning, to guide readers’ intuitions away from first impressions to understand how the term is used in our field. Second, as a reader, you need to be on the look-out for hidden technical terms, especially when you’re reading technical work.

I remember making a particularly silly mistake along these lines. It was early on in grad school, back when I knew almost nothing about quantum field theory. One of our classes was a seminar, structured so that each student would give a talk on some topic that could be understood by the whole group. Unfortunately, some grad students with deeper backgrounds in theoretical physics hadn’t quite gotten the memo.

It was a particular phrase that set me off: “This theory isn’t an effective theory”.

My immediate response was to raise my hand. “What’s wrong with it? What about this theory makes it ineffective?”

The presenter boggled for a moment before responding. “Well, it’s complete up to high energies…it has no ultraviolet divergences…”

“Then shouldn’t that make it even more effective?”

After a bit more of this back-and-forth, we finally cleared things up. As it turns out, “effective field theory” is a technical term! An “effective field theory” is only “effectively” true, describing physics at low energies but not at high energies. As you can see, the word “effective” here is definitely pulling its weight, helping to make the concept understandable…but if you don’t recognize it as a technical term and interpret it literally, you’re going to leave everyone confused!

Over time, I’ve gotten better at identifying when something is a technical term. It really is a skill you can learn: there are different tones people use when speaking, different cadences when writing, a sense of uneasiness that can clue you in to a word being used in something other than its literal sense. Without that skill, you end up worried about mathematicians’ motives for their evil schemes. With it, you’re one step closer to what may be the most important skill in science: the ability to recognize something you don’t know yet.

Is Everything Really Astonishingly Simple?

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Neil Turok gave a talk last week, entitled The Astonishing Simplicity of Everything. In it, he argued that our current understanding of physics is really quite astonishingly simple, and that recent discoveries seem to be confirming this simplicity.

For the right sort of person, this can be a very uplifting message. The audience was spellbound. But a few of my friends were pretty thoroughly annoyed, so I thought I’d dedicate a post to explaining why.

Neil’s talk built up to showing this graphic, one of the masterpieces of Perimeter’s publications department:

Looked at in this way, the laws of physics look astonishingly simple. One equation, a few terms, each handily labeled with a famous name of some (occasionally a little hazy) relevance to the symbol in question.

In a sense, the world really is that simple. There are only a few kinds of laws that govern the universe, and the concepts behind them are really, deep down, very simple concepts. Neil adroitly explained some of the concepts behind quantum mechanics in his talk (here represented by the Schrodinger, Feynman, and Planck parts of the equation), and I have a certain fondness for the Maxwell-Yang-Mills part. The other parts represent different kinds of particles, and different ways they can interact.

While there are only a few different kinds of laws, though, that doesn’t mean the existing laws are simple. That nice, elegant equation hides 25 arbitrary parameters, hidden in the Maxwell-Yang-Mills, Dirac, Kobayashi-Masakawa, and Higgs parts. It also omits the cosmological constant, which fuels the expansion of the universe. And there are problems if you try to claim that the gravity part, for example, is complete.

When Neil mentions recent discoveries, he’s referring to the LHC not seeing new supersymmetric particles, to telescopes not seeing any unusual features in the cosmic microwave background. The theories that were being tested, supersymmetry and inflation, are in many ways more complicated than the Standard Model, adding new parameters without getting rid of old ones. But I think it’s a mistake to say that if these theories are ruled out, the world is astonishingly simple. These theories are attempts to explain unlikely features of the old parameters, or unlikely features of the universe we observe. Without them, we’ve still got those unlikely, awkward, complicated bits.

Of course, Neil doesn’t think the Standard Model is all there is either, and while he’s not a fan of inflation, he does have proposals he’s worked on that explain the same observations, proposals that are also beyond the current picture. More broadly, he’s not suggesting here that the universe is just what we’ve figured out so far and no more. Rather, he’s suggesting that new proposals ought to build on the astonishing simplicity of the universe, instead of adding complexity, that we need to go back to the conceptual drawing board rather than correcting the universe with more gears and wheels.

On the one hand, that’s Perimeter’s mission statement in a nutshell. Perimeter’s independent nature means that folks here can focus on deeper conceptual modifications to the laws of physics, rather than playing with the sorts of gears and wheels that people already know how to work with.

On the other hand, a lack of new evidence doesn’t do anyone any favors. It doesn’t show the way for supersymmetry, but it doesn’t point to any of the “deep conceptual” approaches either. And so for some people, Neil’s glee at the lack of new evidence feels less like admiration for the simplicity of the cosmos and more like that one guy in a group project who sits back chuckling while everyone else fails. You can perhaps understand why some people felt resentful.

Why I Spent Convergence Working

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Convergence is basically Perimeter Institute Christmas.

This week, the building was dressed up in festive posters and elaborate chalk art, and filled with Perimeter’s many distant relations. Convergence is like a hybrid of an alumni reunion and a conference, where Perimeter’s former students and close collaborators come to hear talks about the glory of Perimeter and the marvels of its research.

No-One Can Tell You What They Don’t Understand

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On Wednesday, Amanda Peet gave a Public Lecture at Perimeter on string theory and black holes, while I and other Perimeter-folk manned the online chat. If you missed it, it’s recorded online here.

We get a lot of questions in the online chat. Some are quite insightful, some are basic, and some…well, some are kind of strange. Like the person who asked us how holography could be compatible with irrational numbers.

In physics, holography is the idea that you can encode the physics of a wider space using only information on its boundary. If you remember the 90’s or read Buzzfeed a lot, you might remember holograms: weird rainbow-colored images that looked 3d when you turned your head.

On a computer screen, they instead just look awkward.

Holograms in physics are a lot like that, but rather than a 2d image looking like a 3d object, they can be other combinations of dimensions as well. The most famous, AdS/CFT, relates a ten-dimensional space full of strings to a four-dimensional space on its boundary, where the four-dimensional space contains everybody’s favorite theory, N=4 super Yang-Mills.

So from this explanation, it’s probably not obvious what holography has to do with irrational numbers. That’s because there is no connection: holography has nothing to do with irrational numbers.

Naturally, we were all a bit confused, so one of us asked this person what they meant. They responded by asking if we knew what holograms and irrational numbers were. After all, the problem should be obvious then, right?

In this sort of situation, it’s tempting to assume you’re being trolled. In reality, though, the problem was one of the most common in science communication: people can’t tell you what they don’t understand, because they don’t understand it.

When a teacher asks “any questions?”, they’re assuming students will know what they’re missing. But a deep enough misunderstanding doesn’t show itself that way. Misunderstand things enough, and you won’t know you’re missing anything. That’s why it takes real insight to communicate science: you have to anticipate ways that people might misunderstand you.

In this situation, I thought about what associations people have with holograms. While some might remember the rainbow holograms of old, there are other famous holograms that might catch peoples’ attention.

Please state the nature of the medical emergency.

In science fiction, holograms are 3d projections, ways that computers can create objects out of thin air. The connection to a 2d image isn’t immediately apparent, but the idea that holograms are digital images is central.

Digital images are the key, here. A computer has to express everything in a finite number of bits. It can’t express an irrational number, a number with a decimal expansion that goes on to infinity, at least not without tricks. So if you think that holography is about reality being digital, rather than lower-dimensional, then the question makes perfect sense: how could a digital reality contain irrational numbers?

This is the sort of thing we have to keep in mind when communicating science. It’s easy to misunderstand, to take some aspect of what someone said and read it through a different lens. We have to think about how others will read our words, we have to be willing to poke and prod until we root out the source of the confusion. Because nobody is just going to tell us what they don’t get.

Outreach as the End Product of Science

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Sabine Hossenfelder recently wrote a blog post about physics outreach. In it, she identifies two goals: inspiration, and education.

Inspiration outreach is all about making science seem cool. It’s the IFLScience side of things, stoking the science fandom and getting people excited.

Education outreach, by contrast, is about making sure peoples’ beliefs are accurate. It teaches the audience something about the world around them, giving them a better understanding of how the world works.

In both cases, though, Sabine finds it hard to convince other scientists that outreach is valuable. Maybe inspiration helps increase grant funding, maybe education makes people vote better on scientific issues like climate change…but there isn’t a lot of research that shows that outreach really accomplishes either.

Sabine has a number of good suggestions in her post for how to make outreach more effective, but I’d like to take a step back and suggest that maybe we as a community are thinking about outreach in the wrong way. And in order to do that, I’m going to do a little outreach myself, and talk about black holes.

The black hole of physics outreach.

Black holes are collapsed stars, crushed in on themselves by their own gravity so much that one you get close enough (past the event horizon) not even light can escape. This means that if you sent an astronaut past the event horizon, there would be no way for them to communicate with you: any way they might try to get information to you would travel, at most, at the speed of light.

Einstein’s equations keep working fine past the event horizon, but despite that there are some people who view any prediction of what happens inside to be outside the scope of science. If there’s no way to report back, then how could we ever test our predictions? And if we can’t test our predictions, aren’t we missing the cornerstone of science itself?

In a rather entertaining textbook, physicists Edwin F. Taylor and John Archibald Wheeler suggest a way around this: instead of sending just one astronaut, send multiple! Send a whole community! That way, while we might not be able to test our predictions about the inside of the event horizon, the scientific community that falls in certainly can. For them, those predictions aren’t just meaningless speculation, but testable science.

If something seems unsatisfying about this, congratulations: you now understand the purpose of outreach.

As long as scientific advances never get beyond a small community, we’re like Taylor and Wheeler’s astronauts inside the black hole. We can test our predictions among each other, verify them to our heart’s content…but if they never reach the wider mass of humanity, then what have we really accomplished? Have we really created knowledge, when only a few people will ever know it?

In my Who Am I? post, I express the hope that one day the science I blog about will be as well known as electrons and protons. That might sound farfetched, but I really do think it’s possible. In one hundred years, electrons and protons went from esoteric discoveries of a few specialists to something children learn about in grade school. If science is going to live up to its purpose, if we’re going to escape the black hole of our discipline, then in another hundred years quantum field theory needs to do the same. And by doing outreach work, each of us is taking steps in that direction.

What’s the Matter with Dark Matter, Matt?

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It’s very rare that I disagree with Matt Strassler. That said, I can’t help but think that, when he criticizes the press for focusing their LHC stories on dark matter, he’s missing an important element.

From his perspective, when the media says that the goal of the new run of the LHC is to detect dark matter, they’re just being lazy. People have heard of dark matter. They might have read that it makes up 23% of the universe, more than regular matter at 4%. So when an LHC physicist wants to explain what they’re working on to a journalist, the easiest way is to talk about dark matter. And when the journalist wants to explain the LHC to the public, they do the same thing.

This explanation makes sense, but it’s a little glib. What Matt Strassler is missing is that, from the public’s perspective, dark matter really is a central part of the LHC’s justification.

Now, I’m not saying that the LHC’s main goal is to detect dark matter! Directly detecting dark matter is pretty low on the LHC’s list of priorities. Even if it detects a new particle with the right properties to be dark matter, it still wouldn’t be able to confirm that it really is dark matter without help from another experiment that actually observes some consequence of the new particle among the stars. I agree with Matt when he writes that the LHC’s priorities for the next run are

studying the newly discovered Higgs particle in great detail, checking its properties very carefully against the predictions of the “Standard Model” (the equations that describe the known apparently-elementary particles and forces) to see whether our current understanding of the Higgs field is complete and correct, and
trying to find particles or other phenomena that might resolve the naturalness puzzle of the Standard Model, a puzzle which makes many particle physicists suspicious that we are missing an important part of the story, and
seeking either dark matter particles or particles that may be shown someday to be “associated” with dark matter.

Here’s the thing, though:

From the public’s perspective, why do we need to study the properties of the Higgs? Because we think it might be different than the Standard Model predicts.

Why do we think it might be different than the Standard Model predicts? More generally, why do we expect the world to be different from the Standard Model at all? Well there are a few reasons, but they generally boil down to two things: the naturalness puzzle, and the fact that the Standard Model doesn’t have anything that could account for dark matter.

Naturalness is a powerful motivation, but it’s hard to sell to the general public. Does the universe appear fine-tuned? Then maybe it just is fine-tuned! Maybe someone fine-tuned it!

These arguments miss the real problem with fine-tuning, but they’re hard to correct in a short article. Getting the public worried about naturalness is tough, tough enough that I don’t think we can demand it of the average journalist, or accuse them of being lazy if they fail to do it.

That leaves dark matter. And for all that naturalness is philosophically murky, dark matter is remarkably clear. We don’t know what 96% of the universe is made of! That’s huge, and not just in a “gee-whiz-cool” way. It shows, directly and intuitively, that physics still has something it needs to solve, that we still have particles to find. Unless you are a fan of (increasingly dubious) modifications to gravity like MOND, dark matter is the strongest possible justification for machines like the LHC.

The LHC won’t confirm dark matter on its own. It might not directly detect it, that’s still quite up-in-the-air. And even if it finds deviations from the Standard Model, it’s not likely they’ll be directly caused by dark matter, at least not in a simple way.

But the reason that the press is describing the LHC’s mission in terms of dark matter isn’t just laziness. It’s because, from the public’s perspective, dark matter is the only vaguely plausible reason to spend billions of dollars searching for new particles, especially when we’ve already found the Higgs. We’re lucky it’s such a good reason.

Only the Boring Kind of Parallel Universes

What Counts as a Fundamental Force?

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I’m giving a presentation next Wednesday for Learning Unlimited, an organization that presents educational talks to seniors in Woodstock, Ontario. The talk introduces the fundamental forces and talks about Yang and Mills before moving on to introduce my work.

While practicing the talk today, someone from Perimeter’s outreach department pointed out a rather surprising missing element: I never mention gravity!

Most people know that there are four fundamental forces of nature. There’s Electromagnetism, there’s Gravity, there’s the Weak Nuclear Force, and there’s the Strong Nuclear Force.

Listed here by their most significant uses.

What ties these things together, though? What makes them all “fundamental forces”?

Mathematically, gravity is the odd one out here. Electromagnetism, the Weak Force, and the Strong Force all share a common description: they’re Yang-Mills forces. Gravity isn’t. While you can sort of think of it as a Yang-Mills force “squared”, it’s quite a bit more complicated than the Yang-Mills forces.

You might be objecting that the common trait of the fundamental forces is obvious: they’re forces! And indeed, you can write down a force law for gravity, and a force law for E&M, and umm…

[Mumble Mumble]

Ok, it’s not quite as bad as xkcd would have us believe. You can actually write down a force law for the weak force, if you really want to, and it’s at least sort of possible to talk about the force exerted by the strong interaction.

All that said, though, why are we thinking about this in terms of forces? Forces are a concept from classical mechanics. For a beginning physics student, they come up again and again, in free-body diagram after free-body diagram. But by the time a student learns quantum mechanics, and quantum field theory, they’ve already learned other ways of framing things where forces aren’t mentioned at all. So while forces are kind of familiar to people starting out, they don’t really match onto anything that most quantum field theorists work with, and it’s a bit weird to classify things that only really appear in quantum field theory (the Weak Nuclear Force, the Strong Nuclear Force) based on whether or not they’re forces.

Isn’t there some connection, though? After all, gravity, electromagnetism, the strong force, and the weak force may be different mathematically, but at least they all involve bosons.

Well, yes. And so does the Higgs.

The Higgs is usually left out of listings of the fundamental forces, because it’s not really a “force”. It doesn’t have a direction, instead it works equally at every point in space. But if you include spin 2 gravity and spin 1 Yang-Mills forces, why not also include the spin 0 Higgs?

Well, if you’re doing that, why not include fermions as well? People often think of fermions as “matter” and bosons as “energy”, but in fact both have energy, and neither is made of it. Electrons and quarks are just as fundamental as photons and gluons and gravitons, just as central a part of how the universe works.

I’m still trying to decide whether my presentation about Yang-Mills forces should also include gravity. On the one hand, it would make everything more familiar. On the other…pretty much this entire post.

4 gravitons

Stories about physics from someone who's been there