# Underdetermination of Theory by Metaphor

Sometimes I explain science in unconventional ways. I’ll talk about quantum mechanics without ever using the word “measurement”, or write the action of the Standard Model in legos.

Whenever I do this, someone asks me why. Why use a weird, unfamiliar explanation? Why not just stick to the tried and true, metaphors that have been tested and honed in generations of popular science books?

It’s not that I have a problem with the popular explanations, most of the time. It’s that, even when the popular explanation does a fine job, there can be good reason to invent a new metaphor. To demonstrate my point, here’s a new metaphor to explain why:

In science, we sometimes talk about underdetermination of a theory by the data. We want to find a theory whose math matches the experimental results, but sometimes the experiments just don’t tell us enough. If multiple theories match the data, we say that the theory is underdetermined, and we go looking for more data to resolve the problem.

What if you’re not a scientist, though? Often, that means you hear about theories secondhand, from some science popularizer. You’re not hearing the full math of the theory, you’re not seeing the data. You’re hearing metaphors and putting together your own picture of the theory. Metaphors are your data, in some sense. And just as scientists can find their theories underdetermined by the experimental data, you can find them underdetermined by the metaphors.

This can happen if a metaphor is consistent with two very different interpretations. If you hear that time runs faster in lower gravity, maybe you picture space and time as curved…or maybe you think low gravity makes you skip ahead, so you end up in the “wrong timeline”. Even if the popularizer you heard it from was perfectly careful, you base your understanding of the theory on the metaphor, and you can end up with the wrong understanding.

In science, the only way out of underdetermination of a theory is new, independent data. In science popularization, it’s new, independent metaphors. New metaphors shake you out of your comfort zone. If you misunderstood the old metaphor, now you’ll try to fit that misunderstanding with the new metaphor too. Often, that won’t work: different metaphors lead to different misunderstandings. With enough different metaphors, your picture of the theory won’t be underdetermined anymore: there will be only one picture, one understanding, that’s consistent with every metaphor.

That’s why I experiment with metaphors, why I try new, weird explanations. I want to wake you up, to make sure you aren’t sticking to the wrong understanding. I want to give you more data to determine your theory.

# Journalists Need to Adapt to Preprints, Not Ignore Them

On the surface, this is a bit like an article by foxes decrying the dangers of henhouses. There’s a pretty big conflict of interest when a journal like Nature, that makes huge amounts of money out of research scientists would be happy to publish for free, gets snippy about scientists sharing their work elsewhere. I was expecting an article about how “important” the peer review process is, how we can’t just “let anyone” publish, and the like.

Instead, I was pleasantly surprised. The article is about a real challenge, the weakening of journalistic embargoes. While this is still a problem I think journalists can think their way around, it’s a bit subtler than the usual argument.

For the record, peer review is usually presented as much more important than it actually is. When a scientific article gets submitted to a journal, it gets sent to two or three experts in the field for comment. In the best cases, these experts read the paper carefully and send criticism back. They don’t replicate the experiments, they don’t even (except for a few heroic souls) reproduce the calculations. That kind of careful reading is important, but it’s hardly unique: it’s something scientists do on their own when they want to build off of someone else’s paper, and it’s what good journalists get when they send a paper to experts for comments before writing an article. If peer review in a journal is important, it’s to ensure that this careful reading happens at least once, a sort of minimal evidence that the paper is good enough to appear on a scientist’s CV.

The Nature article points out that peer review serves another purpose, specifically one of delay. While a journal is preparing to publish an article they can send it out to journalists, after making them sign an agreement (an embargo) that they won’t tell the public until the journal publishes. This gives the journalists a bit of lead time, so the more responsible ones can research and fact-check before publishing.

Open-access preprints cut out the lead time. If the paper just appears online with no warning and no embargoes, journalists can write about it immediately. The unethical journalists can skip fact-checking and publish first, and the ethical ones have to follow soon after, or risk publishing “old news”. Nobody gets the time to properly vet, or understand, a new paper.

There’s a simple solution I’ve seen from a few folks on Twitter: “Don’t be an unethical journalist!” That doesn’t actually solve the problem though. The question is, if you’re an ethical journalist, but other people are unethical journalists, what do you do?

Apparently, what some ethical journalists do is to carry on as if preprints didn’t exist. The Nature article describes journalists who, after a preprint has been covered extensively by others, wait until a journal publishes it and then cover it as if nothing had happened. The article frames this as virtuous, but doomed: journalists sticking to their ethics even if it means publishing “old news”.

To be 100% clear here, this is not virtuous. If you present a paper’s publication in a journal as news, when it was already released as a preprint, you are actively misleading the public. I can’t count the number of times I’ve gotten messages from readers, confused because they saw a scientific result covered again months later and thought it was new. It leads to a sort of mental “double-counting”, where the public assumes that the scientific result was found twice, and therefore that it’s more solid. Unless the publication itself is unexpected (something that wasn’t expected to pass peer review, or something controversial like Mochizuki’s proof of the ABC conjecture) mere publication in a journal of an already-public result is not news.

What science journalists need to do here is to step back, and think about how their colleagues cover stories. Current events these days don’t have embargoes, they aren’t fed through carefully managed press releases. There’s a flurry of initial coverage, and it gets things wrong and misses details and misleads people, because science isn’t the only field that’s complicated, real life is complicated. Journalists have adapted to this schedule, mostly, by specializing. Some journalists and news outlets cover breaking news as it happens, others cover it later with more in-depth analysis. Crucially, the latter journalists don’t present the topic as new. They write explicitly in the light of previous news, as a response to existing discussion. That way, the public isn’t misled, and their existing misunderstandings can be corrected.

The Nature article brings up public health, and other topics where misunderstandings can do lasting damage, as areas where embargoes are useful. While I agree, I would hope many of these areas would figure out embargoes on their own. My field certainly does: the big results of scientific collaborations aren’t just put online as preprints, they’re released only after the collaboration sets up its own journalistic embargoes, and prepares its own press releases. In a world of preprints, this sort of practice needs to happen for important controversial public health and environmental results as well. Unethical scientists might still release too fast, to keep journalists from fact-checking, but they could do that anyway, without preprints. You don’t need a preprint to call a journalist on the phone and claim you cured cancer.

As open-access preprints become the norm, journalists will have to adapt. I’m confident they will be able to, but only if they stop treating science journalism as unique, and start treating it as news. Science journalism isn’t teaching, you’re not just passing down facts someone else has vetted. You’re asking the same questions as any other journalist: who did what? And what really happened? If you can do that, preprints shouldn’t be scary.

# Citations Are Reblogs

Last week we had a seminar from Nadav Drukker, a physicist who commemorates his papers with pottery.

At the speaker dinner we got to chatting about physics outreach, and one of my colleagues told an amusing story. He was explaining the idea of citations to someone at a party, and the other person latched on to the idea of citations as “likes” on Facebook. She was then shocked when he told her that a typical paper of his got around fifty citations.

“Only fifty likes???”

Ok, clearly the metaphor of citations as “likes” is more than a little silly. Liking a post is easy and quick, while citing a paper requires a full paper of your own. Obviously, citations are not “likes”.

No, citations are reblogs.

Citations are someone engaging with your paper, your “post” in this metaphor, and building on it, making it part of their own work. That’s much closer to a “reblog” (or in Facebook terms a “share”) than a “like”. More specifically, it’s a “reblog-with-commentary”, taking someone’s content and adding your own, in a way that acknowledges where the original idea came from. And while fifty “likes” on a post may seem low, fifty reblogs with commentary (not just “LOL SMH”, but actual discussion) is pretty reasonable.

The average person doesn’t know much about academia, but there are a lot of academia-like communities out there. People who’ve never written a paper might know what it’s like to use characters from someone else’s fanfiction, or sew a quilt based on a friend’s pattern. Small communities of creative people aren’t so different from each other, whether they’re writers or gamers or scientists. Each group has traditions of building on each other’s work, acknowledging where your inspiration came from, and using that to build standing in the community. Citations happen to be ours.

# Seeing the Wires in Science Communication

Recently, I’ve been going to Science and Cocktails, a series of popular science lectures in Freetown Christiania. The atmosphere is great fun, but I’ve been finding the lectures themselves a bit underwhelming. It’s mostly my fault, though.

There’s a problem, common to all types of performing artists. Once you know the tricks that make a performance work, you can’t un-see them. Do enough theater and you can’t help but notice how an actor interprets their lines, or how they handle Shakespeare’s dirty jokes. Play an instrument, and you think about how they made that sound, or when they pause for breath. Work on action movies, and you start to see the wires.

This has been happening to me with science communication. Going to the Science and Cocktails lectures, I keep seeing the tricks the speaker used to make the presentation easier. I notice the slides that were probably copied from the speaker’s colloquiums, sometimes without adapting them to the new audience. I notice when an example doesn’t really fit the narrative, but is wedged in there anyway because the speaker wants to talk about it. I notice filler, like a recent speaker who spent several slides on the history of electron microscopes, starting with Hooke!

I’m not claiming I’m a better speaker than these people. The truth is, I notice these tricks because I’ve been guilty of them myself! I reuse slides, I insert pet topics, I’ve had talks that were too short until I added a long historical section.

And overall, it doesn’t seem to matter. The audience doesn’t notice our little shortcuts, just like they didn’t notice the wires in old kung-fu movies. They’re there for the magic of the performance, they want to be swept away by a good story.

I need to reconnect with that. It’s still important to avoid using blatant tricks, to cover up the wires and make things that much more seamless. But in the end, what matters is whether the audience learned something, and whether they had a good time. I need to watch not just the tricks, but the magic: what makes the audience’s eyes light up, what makes them laugh, what makes them think. I need to stop griping about the wires, and start seeing the action.

# Path Integrals and Loop Integrals: Different Things!

When talking science, we need to be careful with our words. It’s easy for people to see a familiar word and assume something totally different from what we intend. And if we use the same word twice, for two different things…

I’ve noticed this problem with the word “integral”. When physicists talk about particle physics, there are two kinds of integrals we mention: path integrals, and loop integrals. I’ve seen plenty of people get confused, and assume that these two are the same thing. They’re not, and it’s worth spending some time explaining the difference.

Let’s start with path integrals (also referred to as functional integrals, or Feynman integrals). Feynman promoted a picture of quantum mechanics in which a particle travels along many different paths, from point A to point B.

You’ve probably seen a picture like this. Classically, a particle would just take one path, the shortest path, from A to B. In quantum mechanics, you have to add up all possible paths. Most longer paths cancel, so on average the short, classical path is the most important one, but the others do contribute, and have observable, quantum effects. The sum over all paths is what we call a path integral.

It’s easy enough to draw this picture for a single particle. When we do particle physics, though, we aren’t usually interested in just one particle: we want to look at a bunch of different quantum fields, and figure out how they will interact.

We still use a path integral to do that, but it doesn’t look like a bunch of lines from point A to B, and there isn’t a convenient image I can steal from Wikipedia for it. The quantum field theory path integral adds up, not all the paths a particle can travel, but all the ways a set of quantum fields can interact.

How do we actually calculate that?

One way is with Feynman diagrams, and (often, but not always) loop integrals.

I’ve talked about Feynman diagrams before. Each one is a picture of one possible way that particles can travel, or that quantum fields can interact. In some (loose) sense, each one is a single path in the path integral.

Each diagram serves as instructions for a calculation. We take information about the particles, their momenta and energy, and end up with a number. To calculate a path integral exactly, we’d have to add up all the diagrams we could possibly draw, to get a sum over all possible paths.

(There are ways to avoid this in special cases, which I’m not going to go into here.)

Sometimes, getting a number out of a diagram is fairly simple. If the diagram has no closed loops in it (if it’s what we call a tree diagram) then knowing the properties of the in-coming and out-going particles is enough to know the rest. If there are loops, though, there’s uncertainty: you have to add up every possible momentum of the particles in the loops. You do that with a different integral, and that’s the one that we sometimes refer to as a loop integral. (Perhaps confusingly, these are also often called Feynman integrals: Feynman did a lot of stuff!)

$\frac{i^{a+l(1-d/2)}\pi^{ld/2}}{\prod_i \Gamma(a_i)}\int_0^\infty...\int_0^\infty \prod_i\alpha_i^{a_i-1}U^{-d/2}e^{iF/U-i\sum m_i^2\alpha_i}d\alpha_1...d\alpha_n$

Loop integrals can be pretty complicated, but at heart they’re the same sort of thing you might have seen in a calculus class. Mathematicians are pretty comfortable with them, and they give rise to numbers that mathematicians find very interesting.

Path integrals are very different. In some sense, they’re an “integral over integrals”, adding up every loop integral you could write down. Mathematicians can define path integrals in special cases, but it’s still not clear that the general case, the overall path integral picture we use, actually makes rigorous mathematical sense.

So if you see physicists talking about integrals, it’s worth taking a moment to figure out which one we mean. Path integrals and loop integrals are both important, but they’re very, very different things.

# The Rippling Pond Universe

[Background: Someone told me they couldn’t imagine popularizing Quantum Field Theory in the same flashy way people popularize String Theory. Naturally I took this as a challenge. Please don’t take any statements about what “really exists” here too seriously, this isn’t intended as metaphysics, just metaphor.]

You probably learned about atoms in school.

Your teacher would have explained that these aren’t the same atoms the ancient Greeks imagined. Democritus thought of atoms as indivisible, unchanging spheres, the fundamental constituents of matter. We know, though, that atoms aren’t indivisible. They’re clouds of electrons, buzzing in their orbits around a nucleus of protons and neutrons. Chemists can divide the electrons from the rest, nuclear physicists can break the nucleus. The atom is not indivisible.

And perhaps your teacher remarked on how amazing it is, that the nucleus is such a tiny part of the atom, that the atom, and thus all solid matter, is mostly empty space.

You might have learned that protons and neutrons, too, are not indivisible. That each proton, and each neutron, is composed of three particles called quarks, particles which can be briefly freed by powerful particle colliders.

And you might have wondered, then, even if you didn’t think to ask: are quarks atoms? The real atoms, the Greek atoms, solid indestructible balls of fundamental matter?

They aren’t, by the way.

You might have gotten an inkling of this, learning about beta decay. In beta decay, a neutron transforms, becoming a proton, an electron, and a neutrino. Look for an electron inside a neutron, and you won’t find one. Even if you look at the quarks, you see the same transformation: a down quark becomes an up quark, plus an electron, plus a neutrino. If quarks were atoms, indivisible and unchanging, this couldn’t happen. There’s nowhere for the electron to hide.

In fact, there are no atoms, not the way the Greeks imagined. Just ripples.

Picture the universe as a pond. This isn’t a still pond: something has disturbed it, setting ripples and whirlpools in motion. These ripples and whirlpools skim along the surface of the pond, eddying together and scattering apart.

Our universe is not a simple pond, and so these are not simple ripples. They shine and shimmer, each with their own bright hue, colors beyond our ordinary experience that mix in unfamiliar ways. The different-colored ripples interact, merge and split, and the pond glows with their light.

Stand back far enough, and you notice patterns. See that red ripple, that stays together and keeps its shape, that meets other ripples and interacts in predictable ways. You might imagine the red ripple is an atom, truly indivisible…until it splits, transforms, into ripples of new colors. The quark has changed, down to up, an electron and a neutrino rippling away.

All of our world is encoded in the colors of these ripples, each kind of charge its own kind of hue. With a wink (like your teacher’s, telling you of empty atoms), I can tell you that distance itself is just a kind of ripple, one that links other ripples together. The pond’s very nature as a place is defined by the ripples on it.

This is Quantum Field Theory, the universe of ripples. Democritus said that in truth there are only atoms and the void, but he was wrong. There are no atoms. There is only the void. It ripples and shimmers, and each of us lives as a collection of whirlpools, skimming the surface, seeming concrete and real and vital…until the ripples dissolve, and a new pattern comes.

# The Quantum Kids

I gave a pair of public talks at the Niels Bohr International Academy this week on “The Quest for Quantum Gravity” as part of their “News from the NBIA” lecture series. The content should be familiar to long-time readers of this blog: I talked about renormalization, and gravitons, and the whole story leading up to them.

(I wanted to title the talk “How I Learned to Stop Worrying and Love Quantum Gravity”, like my blog post, but was told Danes might not get the Doctor Strangelove reference.)

I also managed to work in some history, which made its way into the talk after Poul Damgaard, the director of the NBIA, told me I should ask the Niels Bohr Archive about Gamow’s Thought Experiment Device.

“What’s a Thought Experiment Device?”

This, apparently

If you’ve heard of George Gamow, you’ve probably heard of the Alpher-Bethe-Gamow paper, his work with grad student Ralph Alpher on the origin of atomic elements in the Big Bang, where he added Hans Bethe to the paper purely for an alpha-beta-gamma pun.

As I would learn, Gamow’s sense of humor was prominent quite early on. As a research fellow at the Niels Bohr Institute (essentially a postdoc) he played with Bohr’s kids, drew physics cartoons…and made Thought Experiment Devices. These devices were essentially toy experiments, apparatuses that couldn’t actually work but that symbolized some physical argument. The one I used in my talk, pictured above, commemorated Bohr’s triumph over one of Einstein’s objections to quantum theory.

Learning more about the history of the institute, I kept noticing the young researchers, the postdocs and grad students.

Lev Landau, George Gamow, Edward Teller. The kids are Aage and Ernest Bohr. Picture from the Niels Bohr Archive.

We don’t usually think about historical physicists as grad students. The only exception I can think of is Feynman, with his stories about picking locks at the Manhattan project. But in some sense, Feynman was always a grad student.

This was different. This was Lev Landau, patriarch of Russian physics, crowning name in a dozen fields and author of a series of textbooks of legendary rigor…goofing off with Gamow. This was Edward Teller, father of the Hydrogen Bomb, skiing on the institute lawn.

These were the children of the quantum era. They came of age when the laws of physics were being rewritten, when everything was new. Starting there, they could do anything, from Gamow’s cosmology to Landau’s superconductivity, spinning off whole fields in the new reality.

On one level, I envy them. It’s possible they were the last generation to be on the ground floor of a change quite that vast, a shift that touched all of physics, the opportunity to each become gods of their own academic realms.

I’m glad to know about them too, though, to see them as rambunctious grad students. It’s all too easy to feel like there’s an unbridgeable gap between postdocs and professors, to worry that the only people who make it through seem to have always been professors at heart. Seeing Gamow and Landau and Teller as “quantum kids” dispels that: these are all-too-familiar grad students and postdocs, joking around in all-too-familiar ways, who somehow matured into some of the greatest physicists of their era.