Particles vs Waves, Particles vs Strings

On my “Who Am I?” page, I open with my background, calling myself a string theorist, then clarify: “in practice I’m more of a Particle Theorist, describing the world not in terms of short lengths of string but rather with particles that each occupy a single point in space”.

When I wrote that I didn’t think it would confuse people. Now that I’m older and wiser, I know people can be confused in a variety of ways. And since I recently saw someone confused about this particular phrase (yes I’m vagueblogging, but I suspect you’re reading this and know who you are 😉 ), I figured I’d explain it.

If you’ve learned a few things about quantum mechanics, maybe you have this slogan in mind:

“What we used to think of as particles are really waves. They spread out over an area, with peaks and troughs that interfere, and you never know exactly where you will measure them.”

With that in mind, my talk of “particles that each occupy a single point” doesn’t make sense. Doesn’t the slogan mean that particles don’t exist?

Here’s the thing: that’s the wrong slogan. The right slogan is just a bit different:

“What we used to think of as particles are ALSO waves. They spread out over an area, with peaks and troughs that interfere, and you never know exactly where you will measure them.”

The principle you were remembering is often called “wave-particle duality“. That doesn’t mean “particles don’t exist”. It means “waves and particles are the same thing”.

This matters, because just as wave-like properties are important, particle-like properties are important. And while it’s true that you can never know exactly where you will measure a particle, it’s also true that it’s useful, and even necessary, to think of it as occupying a single point.

That’s because particles can only affect each other when they’re at the same point. Physicists call this the principle of locality, the idea that there is no real “action at a distance”, everything happens because of something traveling from point A to point B. Wave-particle duality doesn’t change that, it just makes the specific point uncertain. It means you have to add up over every specific point where the particles could have interacted, but each term in your sum has to still involve a specific point: quantum mechanics doesn’t let particles affect each other non-locally.

Strings, in turn, are a little bit different. Strings have length, particles don’t. Particles interact at a point, strings can interact anywhere along the string. Strings introduce a teeny bit of non-locality.

When you compare particles and waves, you’re thinking pre-quantum mechanics, two classical things neither of which is the full picture. When you compare particles and strings, both are quantum, both are also waves. But in a meaningful sense one occupies a single point, and the other doesn’t.

The Pointy-Haired University

We all know what it looks like when office work sucks. Maybe you think of Dilbert, or The Office, or the dozens of other comics and shows with the same theme. You picture characters like Dilbert’s Pointy-Haired Boss, stupid and controlling, terrible people with far too much power.

Pictured: what you picture

What does it look like when grad school sucks?

There aren’t a lot of comics, or shows, about grad school. The main one I can think of is PHD Comics.

There are a few characters like the Pointy-Haired Boss in PHD Comics, who are just genuinely bad people, in particular the main character’s advisor Professor Smith. But for the most part, the dysfunction the comic depicts is subtler. Characters aren’t selfish so much as oblivious, they aren’t demanding out of malice but out of misplaced expectations, they’re ineffective not due to incompetence but to understandable human weaknesses.

The comic gets this mostly right. If you’re struggling in grad school, you might have a Pointy-Haired Advisor. But more likely, you’re surrounded by well-meaning, reasonable, intelligent people, who nevertheless are somehow making your life a living hell.

In that situation, it can be tempting to blame yourself. You instinctively look for someone at fault, some terrible person who’s causing the problem, and nobody knows your own faults better than you do.

But before you blame yourself, consider another possibility. Consider that there aren’t just Pointy-Haired Bosses, but Pointy-Haired Institutions. Start with the wrong rules, the wrong incentives, the wrong access to information and accountability, and those well-meaning, intelligent people will end up doing some pretty stupid things. Before deciding you aren’t good enough, ask yourself: is this the only way things could have gone? Instead of a Pointy-Haired Advisor, or a Pointy-Haired Self, maybe you’re just attending a Pointy-Haired University.

A Non-Amplitudish Solution to an Amplitudish Problem

There was an interesting paper last week, claiming to solve a long-standing problem in my subfield.

I calculate what are called scattering amplitudes, formulas that tell us the chance that two particles scatter off each other. Formulas like these exist for theories like the strong nuclear force, called Yang-Mills theories, they also exist for the hypothetical graviton particles of gravity. One of the biggest insights in scattering amplitude research in the last few decades is that these two types of formulas are tied together: as we like to say, gravity is Yang-Mills squared.

A huge chunk of my subfield grew out of that insight. For one, it’s why some of us think we have something useful to say about colliding black holes. But while it’s been used in a dozen different ways, an important element was missing: the principle was never actually proven (at least, not in the way it’s been used).

Now, a group in the UK and the Czech Republic claims to have proven it.

I say “claims” not because I’m skeptical, but because without a fair bit more reading I don’t think I can judge this one. That’s because the group, and the approach they use, isn’t “amplitudish”. They aren’t doing what amplitudes researchers would do.

In the amplitudes subfield, we like to write things as much as possible in terms of measurable, “on-shell” particles. This is in contrast to the older approach that writes things instead in terms of more general quantum fields, with formulas called Lagrangians to describe theories. In part, we avoid the older Lagrangian framing to avoid redundancy: there are many different ways to write a Lagrangian for the exact same physics. We have another reason though, which might seem contradictory: we avoid Lagrangians to stay flexible. There are many ways to rewrite scattering amplitudes that make different properties manifest, and some of the strangest ones don’t seem to correspond to any Lagrangian at all.

If you’d asked me before last week, I’d say that “gravity is Yang-Mills squared” was in that category: something you couldn’t make manifest fully with just a Lagrangian, that you’d need some stranger magic to prove. If this paper is right, then that’s wrong: if you’re careful enough you can prove “gravity is Yang-Mills squared” in the old-school, Lagrangian way.

I’m curious how this is going to develop: what amplitudes people will think about it, what will happen as the experts chime in. For now, as mentioned, I’m reserving judgement, except to say “interesting if true”.

Science as Hermeneutics: Closer Than You’d Think

This post is once again inspired by a Ted Chiang short story. This time, it’s “The Evolution of Human Science”, which imagines a world in which super-intelligent “metahumans” have become incomprehensible to the ordinary humans they’ve left behind. Human scientists in that world practice “hermeneutics“: instead of original research, they try to interpret what the metahumans are doing, reverse-engineering their devices and observing their experiments.

Much like a blogger who, out of ideas, cribs them from books.

It’s a thought-provoking view of what science in the distant future could become. But it’s also oddly familiar.

You might think I’m talking about machine learning here. It’s true that in recent years people have started using machine learning in science, with occasionally mysterious results. There are even a few cases of physicists using machine-learning to suggest some property, say of Calabi-Yau manifolds, and then figuring out how to prove it. It’s not hard to imagine a day when scientists are reduced to just interpreting whatever the AIs throw at them…but I don’t think we’re quite there yet.

Instead, I’m thinking about my own work. I’m a particular type of theoretical physicist. I calculate scattering amplitudes, formulas that tell us the probabilities that subatomic particles collide in different ways. We have a way to calculate these, Feynman’s famous diagrams, but they’re inefficient, so researchers like me look for shortcuts.

How do we find those shortcuts? Often, it’s by doing calculations the old, inefficient way. We use older methods, look at the formulas we get, and try to find patterns. Each pattern is a hint at some new principle that can make our calculations easier. Sometimes we can understand the pattern fully, and prove it should hold. Other times, we observe it again and again and tentatively assume it will keep going, and see what happens if it does.

Either way, this isn’t so different from the hermeneutics scientists practice in the story. Feynman diagrams already “know” every pattern we find, like the metahumans in the story who already know every result the human scientists can discover. But that “knowledge” isn’t in a form we can understand or use. We have to learn to interpret it, to read between the lines and find underlying patterns, to end up with something we can hold in our own heads and put into action with our own hands. The truth may be “out there”, but scientists can’t be content with that. We need to get the truth “in here”. We need to interpret it for ourselves.

Unification That Does Something

I’ve got unification on the brain.

Recently, a commenter asked me what physicists mean when they say two forces unify. While typing up a response, I came across this passage, in a science fiction short story by Ted Chiang.

Physics admits of a lovely unification, not just at the level of fundamental forces, but when considering its extent and implications. Classifications like ‘optics’ or ‘thermodynamics’ are just straitjackets, preventing physicists from seeing countless intersections.

This passage sounds nice enough, but I feel like there’s a misunderstanding behind it. When physicists seek after unification, we’re talking about something quite specific. It’s not merely a matter of two topics intersecting, or describing them with the same math. We already plumb intersections between fields, including optics and thermodynamics. When we hope to find a unified theory, we do so because it does something. A real unified theory doesn’t just aid our calculations, it gives us new ways to alter the world.

To show you what I mean, let me start with something physicists already know: electroweak unification.

There’s a nice series of posts on the old Quantum Diaries blog that explains electroweak unification in detail. I’ll be a bit vaguer here.

You might have heard of four fundamental forces: gravity, electromagnetism, the strong nuclear force, and the weak nuclear force. You might have also heard that two of these forces are unified: the electromagnetic force and the weak nuclear force form something called the electroweak force.

What does it mean that these forces are unified? How does it work?

Zoom in far enough, and you don’t see the electromagnetic force and the weak force anymore. Instead you see two different forces, I’ll call them “W” and “B”. You’ll also see the Higgs field. And crucially, you’ll see the “W” and “B” forces interact with the Higgs.

The Higgs field is special because it has what’s called a “vacuum” value. Even in otherwise empty space, there’s some amount of “Higgsness” in the background, like the color of a piece of construction paper. This background Higgs-ness is in some sense an accident, just one stable way the universe happens to sit. In particular, it picks out an arbitrary kind of direction: parts of the “W” and “B” forces happen to interact with it, and parts don’t.

Now let’s zoom back out. We could, if we wanted, keep our eyes on the “W” and “B” forces. But that gets increasingly silly. As we zoom out we won’t be able to see the Higgs field anymore. Instead, we’ll just see different parts of the “W” and “B” behaving in drastically different ways, depending on whether or not they interact with the Higgs. It will make more sense to talk about mixes of the “W” and “B” fields, to distinguish the parts that are “lined up” with the background Higgs and the parts that aren’t. It’s like using “aft” and “starboard” on a boat. You could use “north” and “south”, but that would get confusing pretty fast.

My cabin is on the west side of the ship…unless we’re sailing east….

What are those “mixes” of the “W” and “B” forces? Why, they’re the weak nuclear force and the electromagnetic force!

This, broadly speaking, is the kind of unification physicists look for. It doesn’t have to be a “mix” of two different forces: most of the models physicists imagine start with a single force. But the basic ideas are the same: that if you “zoom in” enough you see a simpler model, but that model is interacting with something that “by accident” picks a particular direction, so that as we zoom out different parts of the model behave in different ways. In that way, you could get from a single force to all the different forces we observe.

That “by accident” is important here, because that accident can be changed. That’s why I said earlier that real unification lets us alter the world.

To be clear, we can’t change the background Higgs field with current technology. The biggest collider we have can just make a tiny, temporary fluctuation (that’s what the Higgs boson is). But one implication of electroweak unification is that, with enough technology, we could. Because those two forces are unified, and because that unification is physical, with a physical cause, it’s possible to alter that cause, to change the mix and change the balance. This is why this kind of unification is such a big deal, why it’s not the sort of thing you can just chalk up to “interpretation” and ignore: when two forces are unified in this way, it lets us do new things.

Mathematical unification is valuable. It’s great when we can look at different things and describe them in the same language, or use ideas from one to understand the other. But it’s not the same thing as physical unification. When two forces really unify, it’s an undeniable physical fact about the world. When two forces unify, it does something.

Formal Theory and Simulated Experiment

There are two kinds of theoretical physicists. Some, called phenomenologists, make predictions about the real world. Others, the so-called “formal theorists”, don’t. They work with the same kinds of theories as the phenomenologists, quantum field theories of the sort that have been so successful in understanding the subatomic world. But the specific theories they use are different: usually, toy models that aren’t intended to describe reality.

Most people get this is valuable. It’s useful to study toy models, because they help us tackle the real world. But they stumble on another point. Sure, they say, you can study toy models…but then you should call yourself a mathematician, not a physicist.

I’m a “formal theorist”. And I’m very much not a mathematician, I’m definitely a physicist. Let me explain why, with an analogy.

As an undergrad, I spent some time working in a particle physics lab. The lab had developed a new particle detector chip, designed for a future experiment: the International Linear Collider. It was my job to test this chip.

Naturally, I couldn’t test the chip by flinging particles at it. For one, the collider it was designed for hadn’t been built yet! Instead, I had to use simulated input: send in electrical signals that mimicked the expected particles, and see what happens. In effect, I was using a kind of toy model, as a way to understand better how the chip worked.

I hope you agree that this kind of work counts as physics. It isn’t “just engineering” to feed simulated input into a chip. Not when the whole point of that chip is to go into a physics experiment. This kind of work is a large chunk of what an experimental physicist does.

As a formal theorist, my work with toy models is an important part of what a theoretical physicist does. I test out the “devices” of theoretical physics, the quantum-field-theoretic machinery that we use to investigate the world. Without that kind of careful testing on toy models, we’d have fewer tools to work with when we want to understand reality.

Ok, but you might object: an experimental physicist does eventually build the real experiment. They don’t just spend their career on simulated input. If someone only works on formal theory, shouldn’t that at least make them a mathematician, not a physicist?

Here’s the thing, though: after those summers in that lab, I didn’t end up as an experimental physicist. After working on that chip, I didn’t go on to perfect it for the International Linear Collider. But it would be rather bizarre if that, retroactively, made my work in that time “engineering” and not “physics”.

Oh, I should also mention that the International Linear Collider might not ever be built. So, there’s that.

Formal theory is part of physics because it cares directly about the goals of physics: understanding the real world. It is just one step towards that goal, it doesn’t address the real world alone. But neither do the people testing out chips for future colliders. Formal theory isn’t always useful, similarly, planned experiments don’t always get built. That doesn’t mean it’s not physics.

Kicking Students Out of Their Homes During a Pandemic: A Bad Idea

I avoid talking politics on this blog. There are a few issues, though, where I feel not just able, but duty-bound, to speak out. Those are issues affecting graduate students.

This week, US Immigration and Customs Enforcement (ICE) announced that, if a university switched to online courses as a response to COVID-19, international students would have to return to their home countries or transfer to a school that still teaches in-person.

This is already pretty unreasonable for many undergrads. But think about PhD students.

Suppose you’re a foreign PhD student at a US university. Maybe your school is already planning to have classes online this fall, like Harvard is. Maybe your school is planning to have classes in person, but will change its mind a few weeks in, when so many students and professors are infected that it’s clearly unreasonable to continue. Maybe your school never changes its mind, but your state does, and the school has to lock down anyway.

As a PhD student, you likely don’t live in the dorms. More likely you live in a shared house, or an apartment. You’re an independent adult. Your parents aren’t paying for you to go to school. Your school is itself a full-time job, one that pays (as little as the university thinks it can get away with).

What happens when your school goes online? If you need to leave the country?

You’d have to find some way out of your lease, or keep paying for it. You’d have to find a flight on short notice. You’d have to pack up all your belongings, ship or sell anything you can’t store, or find friends to hold on to it.

You’d have to find somewhere to stay in your “home country”. Some could move in with their parents temporarily, many can’t. Some of those who could in other circumstances, shouldn’t if they’re fleeing from an outbreak: their parents are likely older, and vulnerable to the virus. So you have to find a hotel, eventually perhaps a new apartment, far from what was until recently your home.

Reminder: you’re doing all of this on a shoestring budget, because the university pays you peanuts.

Can you transfer instead? In a word, no.

PhD students are specialists. They’re learning very specific things from very specific people. Academics aren’t the sort of omnidisciplinary scientists you see in movies. Bruce Banner or Tony Stark could pick up a new line of research on a whim, real people can’t. This is why, while international students may be good at the undergraduate level, they’re absolutely necessary for PhDs. When only three people in the world study the thing you want to study, you don’t have the luxury of staying in your birth country. And you can’t just transfer schools when yours goes online.

It feels like the people who made this decision didn’t think about any of this. That they don’t think grad students matter, or forgot they exist altogether. It seems frustratingly common for policy that affects grad students to be made by people who know nothing about grad students, and that baffles me. PhDs are a vital part of the academic career, without them universities in their current form wouldn’t even exist. Ignoring them is like if hospital policy ignored residencies.

I hope that this policy gets reversed, or halted, or schools find some way around it. At the moment, anyone starting school in the US this fall is in a very tricky position. And anyone already there is in a worse one.

As usual, I’m going to ask that the comments don’t get too directly political. As a partial measure to tone things down, I’d like to ask you to please avoid mentioning any specific politicians, political parties, or political ideologies. Feel free to talk instead about your own experiences: how this policy is likely to affect you, or your loved ones. Please also feel free to talk more technically on the policy/legal side. I’d like to know what universities can do to work around this, and whether there are plausible paths to change or halt the policy. Please be civil, and be kind to your fellow commenters.

The Parameter Was Inside You All Along

Sabine Hossenfelder had an explainer video recently on how to tell science from pseudoscience. This is a famously difficult problem, so naturally we have different opinions. I actually think the picture she draws is reasonably sound. But while it is a good criterion to tell whether you yourself are doing pseudoscience, it’s surprisingly tricky to apply it to other people.

Hossenfelder argues that science, at its core, is about explaining observations. To tell whether something is science or pseudoscience you need to ask, first, if it agrees with observations, and second, if it is simpler than those observations. In particular, a scientist should prefer models with fewer parameters. If your model has so many parameters that you can fit any observation, you’re not being scientific.

This is a great rule of thumb, one that as Hossenfelder points out forms the basis of a whole raft of statistical techniques. It does rely on one tricky judgement, though: how many parameters does your model actually have?

Suppose I’m one of those wacky theorists who propose a whole new particle to explain some astronomical mystery. Hossenfelder, being more conservative in these things, proposes a model with no new particles. Neither of our models fit the data perfectly. Perhaps my model fits a little better, but after all it has one extra parameter, from the new particle. If we want to compare our models, we should take that into account, and penalize mine.

Here’s the question, though: how do I know that Hossenfelder didn’t start out with more particles, and got rid of them to get a better fit? If she did, she had more parameters than I did. She just fit them away.

The problem here is closely related to one called the look-elsewhere effect. Scientists don’t publish everything they try. An unscrupulous scientist can do a bunch of different tests until one of them randomly works, and just publish that one, making the result look meaningful when really it was just random chance. Even if no individual scientist is unscrupulous, a community can do the same thing: many scientists testing many different models, until one accidentally appears to work.

As a scientist, you mostly know if your motivations are genuine. You know if you actually tried a bunch of different models or had good reasons from the start to pick the one you did. As someone judging other scientists, you often don’t have that luxury. Sometimes you can look at prior publications and see all the other attempts someone made. Sometimes they’ll even tell you explicitly what parameters they used and how they fit them. But sometimes, someone will swear up and down that their model is just the most natural, principled choice they could have made, and they never considered anything else. When that happens, how do we guard against the look-elsewhere effect?

The normal way to deal with the look-elsewhere effect is to consider, not just whatever tests the scientist claims to have done, but all tests they could reasonably have done. You need to count all the parameters, not just the ones they say they varied.

This works in some fields. If you have an idea of what’s reasonable and what’s not, you have a relatively manageable list of things to look at. You can come up with clear rules for which theories are simpler than others, and people will agree on them.

Physics doesn’t have it so easy. We don’t have any pre-set rules for what kind of model is “reasonable”. If we want to parametrize every “reasonable” model, the best we can do are what are called Effective Field Theories, theories which try to describe every possible type of new physics in terms of its effect on the particles we already know. Even there, though, we need assumptions. The most popular effective field theory, called SMEFT, assumes the forces of the Standard Model keep their known symmetries. You get a different model if you relax that assumption, and even that model isn’t the most general: for example, it still keeps relativity intact. Try to make the most general model possible, and you end up waist-deep in parameter soup.

Subjectivity is a dirty word in science…but as far as I can tell it’s the only way out of this. We can try to count parameters when we can, and use statistical tools…but at the end of the day, we still need to make choices. We need to judge what counts as an extra parameter and what doesn’t, which possible models to compare to and which to ignore. That’s going to be dependent on our scientific culture, on fashion and aesthetics, there just isn’t a way around that. The best we can do is own up to our assumptions, and be ready to change them when we need to.

Pseudonymity Matters. I Stand With Slate Star Codex.

Slate Star Codex is one of the best blogs on the net. Written under the pseudonym Scott Alexander, the blog covers a wide variety of topics with a level of curiosity and humility that the rest of us bloggers can only aspire to.

Recently, this has all been jeopardized. A reporter at the New York Times, writing an otherwise positive article, told Scott he was going to reveal his real name publicly. In a last-ditch effort to stop this, Scott deleted his blog.

I trust Scott. When he says that revealing his identity would endanger his psychiatric practice, not to mention the safety of friends and loved ones, I believe him. What’s more, I think working under a pseudonym makes him a better blogger: some of his best insights have come from talking to people who don’t think of him as “the Slate Star Codex guy”.

I don’t know why the Times thinks revealing Scott’s name is a good idea. I do know that there are people out there who view anyone under a pseudonym with suspicion. Compared to Scott, my pseudonym is paper-thin: it’s very easy to find who I am. Still, I have met people who are irked just by that, by the bare fact that I don’t print my real name on this blog.

I think this might be a generational thing. My generation grew up alongside the internet. We’re used to the idea that very little is truly private, that anything made public somewhere risks becoming public everywhere. In that world, writing under a pseudonym is like putting curtains on a house. It doesn’t make us unaccountable: if you break the law behind your curtains the police can get a warrant, similarly Scott’s pseudonym wouldn’t stop a lawyer from tracking him down. All it is, is a filter: a way to have a life of our own, shielded just a little from the whirlwind of the web.

I know there are journalists who follow this blog. If you have contacts in the Times tech section, or know someone who does, please reach out. I want to hope that someone there is misunderstanding the situation, that when things are fully explained they will back down. We have to try.

The Citation Motivation Situation

Citations are the bread and butter of academia, or maybe its prison cigarettes. They link us together, somewhere between a map to show us the way and an informal currency. They’re part of how the world grades us, a measure more objective than letters from our peers but that’s not saying much. It’s clear why we we want to be cited, but why do we cite others?

For more reasons than you’d expect.

First, we cite to respect priority. Since the dawn of science, we’ve kept track not only of what we know, but of who figured it out first. If we use an idea in our paper, we cite its origin: the paper that discovered or invented it. We don’t do this for the oldest and most foundational ideas: nobody cites Einstein for relativity. But if the idea is at all unusual, we make sure to give credit where credit is due.

Second, we cite to substantiate our claims. Academic papers don’t stand on their own: they depend on older proofs and prior discoveries. If we make a claim that was demonstrated in older work, we don’t need to prove it again. By citing the older work, we let the reader know where to look. If they doubt our claim, they can look at the older paper and see what went wrong.

Those two are the most obvious uses of citations, but there are more. Another important use is to provide context. Academic work doesn’t stand alone: we choose what we work on in part based on how it relates to other work. As such, it’s important to cite that other work, to help readers understand our motivation. When we’re advancing the state of the art, we need to tell the reader what that state of the art is. When we’re answering a question or solving a problem, we can cite the paper that asked the question or posed the problem. When we’re introducing a new method or idea, we need to clearly say what’s new about it: how it improves on older, similar ideas.

Scientists are social creatures. While we often have a scientific purpose in mind, citations also follow social conventions. These vary from place to place, field to field, and sub-field to sub-field. Mention someone’s research program, and you might be expected to cite every paper in that program. Cite one of a pair of rivals, and you should probably cite the other one too. Some of these conventions are formalized in the form of “citeware“, software licenses that require citations, rather than payments, to use. Others come from unspoken cultural rules. Citations are a way to support each other, something that can slightly improve another’s job prospects at no real cost to your own. It’s not surprising that they ended up part of our culture, well beyond their pure academic use.