Monthly Archives: April 2024

The Quantum Paths Not Traveled

Before this week’s post: a former colleague of mine from CEA Paris-Saclay, Sylvain Ribault, posted a dialogue last week presenting different perspectives on academic publishing. One of the highlights of my brief time at the CEA were the times I got to chat with Sylvain and others about the future forms academia might take. He showed me a draft of his dialogue a while ago, designed as a way to introduce newcomers to the debate about how, and whether, academics should do peer review. I’ve got a different topic this week so I won’t say much more about it, but I encourage you to take a look!


Matt Strassler has a nice post up about waves and particles. He’s writing to address a common confusion, between two concepts that sound very similar. On the other hand, there are the waves of quantum field theory, ripples in fundamental fields the smallest versions of which correspond to particles. (Strassler likes to call them “wavicles”, to emphasize their wavy role.) On the other hand, there are the wavefunctions of quantum mechanics, descriptions of the behavior of one or more interacting particles over time. To distinguish, he points out that wavicles can hurt you, while wavefunctions cannot. Wavicles are the things that collide and light up detectors, one by one, wavefunctions are the math that describes when and how that happens. Many types of wavicles can run into each other one by one, but their interactions can all be described together by a single wavefunction. It’s an important point, well stated.

(I do think he goes a bit too far in saying that the wavefunction is not “an object”, though. That smacks of metaphysics, and I think that’s not worth dabbling in for physicists.)

After reading his post, there’s something that might still confuse you. You’ve probably heard that in quantum mechanics, an electron is both a wave and a particle. Does the “wave” in that saying mean “wavicle”, or “wavefunction”?

A “wave” built out of particles

The gif above shows data from a double-slit experiment, an important type of experiment from the early days of quantum mechanics. These experiments were first conducted before quantum field theory (and thus, before the ideas that Strassler summarizes with “wavicles”). In a double-slit experiment, particles are shot at a screen through two slits. The particles that hit the screen can travel through one slit or the other.

A double-slit experiment, in diagram form

Classically, you would expect particles shot randomly at the screen to form two piles on the other side, one in front of each slit. Instead, they bunch up into a rippling pattern, the same sort of pattern that was used a century earlier to argue that light was a wave. The peaks and troughs of the wave pass through both slits, and either line up or cancel out, leaving the distinctive pattern.

When it was discovered that electrons do this too, it led to the idea that electrons must be waves as well, despite also being particles. That insight led to the concept of the wavefunction. So the “wave” in the saying refers to wavefunctions.

But electrons can hurt you, and as Strassler points out, wavefunctions cannot. So how can the electron be a wavefunction?

To risk a bit of metaphysics myself, I’ll just say: it can’t. An electron can’t “be” a wavefunction.

The saying, that electrons are both particles and waves, is from the early days of quantum mechanics, when people were confused about what it all meant. We’re still confused, but we have some better ways to talk about it.

As a start, it’s worth noticing that, whenever you measure an electron, it’s a particle. Each electron that goes through the slits hits your screen as a particle, a single dot. If you see many electrons at once, you may get the feeling that they look like waves. But every actual electron you measure, every time you’re precise enough to notice, looks like a particle. And for each individual electron, you can extrapolate back the path it took, exactly as if it traveled like a particle the whole way through.

The same is true, though, of light! When you see light, photons enter your eyes, and each one that you see triggers a chemical change in a molecule called a photopigment. The same sort of thing happens for photographs, while an electrical signal gets triggered instead in a digital camera. Light may behave like a wave in some sense, but every time you actually observe it it looks like a particle.

But while you can model each individual electron, or photon, as a classical particle, you can’t model the distribution of multiple electrons that way.

That’s because in quantum mechanics, the “paths not taken” matter. A single electron will only go through one slit in the double-slit experiment. But the fact that it could have gone through both slits matters, and changes the chance that it goes through each particular path. The possible paths in the wavefunction interfere with each other, the same way different parts of classical waves do.

That role of the paths not taken, of the “what if”, is the heart and soul of quantum mechanics. No matter how you interpret its mysteries, “what if” matters. If you believe in a quantum multiverse, you think every “what if” happens somewhere in that infinity of worlds. If you think all that matters is observations, then “what if” shows the folly of modeling the world as anything else. If you are tempted to try to mend quantum mechanics with faster-than-light signals, then you have to declare one “what if” the true one. And if you want to double-down on determinism and replace quantum mechanics, you need to declare that certain “what if” questions are off-limits.

“What if matters” isn’t the same as a particle traveling every path at once, it’s its own weird thing with its own specific weird consequences. It’s a metaphor, because everything written in words is a metaphor. But it’s a better metaphor than thinking an electron is both a particle and a wave.

No Unmoved Movers

Economists must find academics confusing.

When investors put money in a company, they have some control over what that company does. They vote to decide a board, and the board votes to hire a CEO. If the company isn’t doing what the investors want, the board can fire the CEO, or the investors can vote in a new board. Everybody is incentivized to do what the people who gave the money want to happen. And usually, those people want the company to increase its profits, since most of them people are companies with their own investors).

Academics are paid by universities and research centers, funded in the aggregate by governments and student tuition and endowments from donors. But individually, they’re also often funded by grants.

What grant-givers want is more ambiguous. The money comes in big lumps from governments and private foundations, which generally want something vague like “scientific progress”. The actual decision of who gets the money are made by committees made up of senior scientists. These people aren’t experts in every topic, so they have to extrapolate, much as investors have to guess whether a new company will be profitable based on past experience. At their best, they use their deep familiarity with scientific research to judge which projects are most likely to work, and which have the most interesting payoffs. At their weakest, though, they stick with ideas they’ve heard of, things they know work because they’ve seen them work before. That, in a nutshell, is why mainstream research prevails: not because the mainstream wants to suppress alternatives, but because sometimes the only way to guess if something will work is raw familiarity.

(What “works” means is another question. The cynical answers are “publishes papers” or “gets citations”, but that’s a bit unfair: in Europe and the US, most funders know that these numbers don’t tell the whole story. The trivial answer is “achieves what you said it would”, but that can’t be the whole story, because some goals are more pointless than others. You might want the answer to be “benefits humanity”, but that’s almost impossible to judge. So in the end the answer is “sounds like good science”, which is vulnerable to all the fads you can imagine…but is pretty much our only option, regardless.)

So are academics incentivized to do what the grant committees want? Sort of.

Science never goes according to plan. Grant committees are made up of scientists, so they know that. So while many grants have a review process afterwards to see whether you achieved what you planned, they aren’t all that picky about it. If you can tell a good story, you can explain why you moved away from your original proposal. You can say the original idea inspired a new direction, or that it became clear that a new approach was necessary. I’ve done this with an EU grant, and they were fine with it.

Looking at this, you might imagine that an academic who’s a half-capable storyteller could get away with anything they wanted. Propose a fashionable project, work on what you actually care about, and tell a good story afterwards to avoid getting in trouble. As long as you’re not literally embezzling the money (the guy who was paying himself rent out of his visitor funding, for instance), what could go wrong? You get the money without the incentives, you move the scientific world and nobody gets to move you.

It’s not quite that easy, though.

Sabine Hossenfelder told herself she could do something like this. She got grants for fashionable topics she thought were pointless, and told herself she’d spend time on the side on the things she felt were actually important. Eventually, she realized she wasn’t actually doing the important things: the faddish research ended up taking all her time. Not able to get grants doing what she actually cared about (and, in one of those weird temporary European positions that only lasts until you run out of grants), she now has to make a living from her science popularization work.

I can’t speak for Hossenfelder, but I’ve also put some thought into how to choose what to research, about whether I could actually be an unmoved mover. A few things get in the way:

First, applying for grants doesn’t just take storytelling skills, it takes scientific knowledge. Grant committees aren’t experts in everything, but they usually send grants to be reviewed by much more appropriate experts. These experts will check if your grant makes sense. In order to make the grant make sense, you have to know enough about the faddish topic to propose something reasonable. You have to keep up with the fad. You have to spend time reading papers, and talking to people in the faddish subfield. This takes work, but also changes your motivation. If you spend time around people excited by an idea, you’ll either get excited too, or be too drained by the dissonance to get any work done.

Second, you can’t change things that much. You still need a plausible story as to how you got from where you are to where you are going.

Third, you need to be a plausible person to do the work. If the committee looks at your CV and sees that you’ve never actually worked on the faddish topic, they’re more likely to give a grant to someone who’s actually worked on it.

Fourth, you have to choose what to do when you hire people. If you never hire any postdocs or students working on the faddish topic, then it will be very obvious that you aren’t trying to research it. If you do hire them, then you’ll be surrounded by people who actually care about the fad, and want your help to understand how to work with it.

Ultimately, to avoid the grant committee’s incentives, you need a golden tongue and a heart of stone, and even then you’ll need to spend some time working on something you think is pointless.

Even if you don’t apply for grants, even if you have a real permanent position or even tenure, you still feel some of these pressures. You’re still surrounded by people who care about particular things, by students and postdocs who need grants and jobs and fellow professors who are confident the mainstream is the right path forward. It takes a lot of strength, and sometimes cruelty, to avoid bowing to that.

So despite the ambiguous rules and lack of oversight, academics still respond to incentives: they can’t just do whatever they feel like. They aren’t bound by shareholders, they aren’t expected to make a profit. But ultimately, the things that do constrain them, expertise and cognitive load, social pressure and compassion for those they mentor, those can be even stronger.

I suspect that those pressures dominate the private sector as well. My guess is that for all that companies think of themselves as trying to maximize profits, the all-too-human motivations we share are more powerful than any corporate governance structure or org chart. But I don’t know yet. Likely, I’ll find out soon.

The Hidden Higgs

Peter Higgs, the theoretical physicist whose name graces the Higgs boson, died this week.

Peter Higgs, after the Higgs boson discovery was confirmed

This post isn’t an obituary: you can find plenty of those online, and I don’t have anything special to say that others haven’t. Reading the obituaries, you’ll notice they summarize Higgs’s contribution in different ways. Higgs was one of the people who proposed what today is known as the Higgs mechanism, the principle by which most (perhaps all) elementary particles gain their mass. He wasn’t the only one: Robert Brout and François Englert proposed essentially the same idea in a paper that was published two months earlier, in August 1964. Two other teams came up with the idea slightly later than that: Gerald Guralnik, Carl Richard Hagen, and Tom Kibble were published one month after Higgs, while Alexander Migdal and Alexander Polyakov found the idea independently in 1965 but couldn’t get it published till 1966.

Higgs did, however, do something that Brout and Englert didn’t. His paper doesn’t just propose a mechanism, involving a field which gives particles mass. It also proposes a particle one could discover as a result. Read the more detailed obituaries, and you’ll discover that this particle was not in the original paper: Higgs’s paper was rejected at first, and he added the discussion of the particle to make it more interesting.

At this point, I bet some of you are wondering what the big deal was. You’ve heard me say that particles are ripples in quantum fields. So shouldn’t we expect every field to have a particle?

Tell that to the other three Higgs bosons.

Electromagnetism has one type of charge, with two signs: plus, and minus. There are electrons, with negative charge, and their anti-particles, positrons, with positive charge.

Quarks have three types of charge, called colors: red, green, and blue. Each of these also has two “signs”: red and anti-red, green and anti-green, and blue and anti-blue. So for each type of quark (like an up quark), there are six different versions: red, green, and blue, and anti-quarks with anti-red, anti-green, and anti-blue.

Diagram of the colors of quarks

When we talk about quarks, we say that the force under which they are charged, the strong nuclear force, is an “SU(3)” force. The “S” and “U” there are shorthand for mathematical properties that are a bit too complicated to explain here, but the “(3)” is quite simple: it means there are three colors.

The Higgs boson’s primary role is to make the weak nuclear force weak, by making the particles that carry it from place to place massive. (That way, it takes too much energy for them to go anywhere, a feeling I think we can all relate to.) The weak nuclear force is an “SU(2)” force. So there should be two “colors” of particles that interact with the weak nuclear force…which includes Higgs bosons. For each, there should also be an anti-color, just like the quarks had anti-red, anti-green, and anti-blue. So we need two “colors” of Higgs bosons, and two “anti-colors”, for a total of four!

But the Higgs boson discovered at the LHC was a neutral particle. It didn’t have any electric charge, or any color. There was only one, not four. So what happened to the other three Higgs bosons?

The real answer is subtle, one of those physics things that’s tricky to concisely explain. But a partial answer is that they’re indistinguishable from the W and Z bosons.

Normally, the fundamental forces have transverse waves, with two polarizations. Light can wiggle along its path back and forth, or up and down, but it can’t wiggle forward and backward. A fundamental force with massive particles is different, because they can have longitudinal waves: they have an extra direction in which they can wiggle. There are two W bosons (plus and minus) and one Z boson, and they all get one more polarization when they become massive due to the Higgs.

That’s three new ways the W and Z bosons can wiggle. That’s the same number as the number of Higgs bosons that went away, and that’s no coincidence. We physicist like to say that the W and Z bosons “ate” the extra Higgs, which is evocative but may sound mysterious. Instead, you can think of it as the two wiggles being secretly the same, mixing together in a way that makes them impossible to tell apart.

The “count”, of how many wiggles exist, stays the same. You start with four Higgs wiggles, and two wiggles each for the precursors of the W+, W-, and Z bosons, giving ten. You end up with one Higgs wiggle, and three wiggles each for the W+, W-, and Z bosons, which still adds up to ten. But which fields match with which wiggles, and thus which particles we can detect, changes. It takes some thought to look at the whole system and figure out, for each field, what kind of particle you might find.

Higgs did that work. And now, we call it the Higgs boson.

Making More Nails

They say when all you have is a hammer, everything looks like a nail.

Academics are a bit smarter than that. Confidently predict a world of nails, and you fall to the first paper that shows evidence of a screw. There are limits to how long you can delude yourself when your job is supposed to be all about finding the truth.

You can make your own nails, though.

Suppose there’s something you’re really good at. Maybe, like many of my past colleagues, you can do particle physics calculations faster than anyone else, even when the particles are super-complicated hypothetical gravitons. Maybe you know more than anyone else about how to make a quantum computer, or maybe you just know how to build a “quantum computer“. Maybe you’re an expert in esoteric mathematics, who can re-phrase anything in terms of the arcane language of category theory.

That’s your hammer. Get good enough with it, and anyone with a nail-based problem will come to you to solve it. If nails are trendy, then you’ll impress grant committees and hiring committees, and your students will too.

When nails aren’t trendy, though, you need to try something else. If your job is secure, and you don’t have students with their own insecure jobs banging down your door, then you could spend a while retraining. You could form a reading group, pick up a textbook or two about screwdrivers and wrenches, and learn how to use different tools. Eventually, you might find a screwdriving task you have an advantage with, something you can once again do better than everyone else, and you’ll start getting all those rewards again.

Or, maybe you won’t. You’ll get less funding to hire people, so you’ll do less research, so your work will get less impressive and you’ll get less funding, and so on and so forth.

Instead of risking that, most academics take another path. They take what they’re good at, and invent new problems in the new trendy area to use that expertise.

If everyone is excited about gravitational waves, you turn a black hole calculation into a graviton calculation. If companies are investing in computation in the here-and-now, then you find ways those companies can use insights from your quantum research. If everyone wants to know how AI works, you build a mathematical picture that sort of looks like one part of how AI works, and do category theory to it.

At first, you won’t be competitive. Your hammer isn’t going to work nearly as well as the screwdrivers people have been using forever for these problems, and there will be all sorts of new issues you have to solve just to get your hammer in position in the first place. But that doesn’t matter so much, as long as you’re honest. Academic research is expected to take time, applications aren’t supposed to be obvious. Grant committees care about what you’re trying to do, as long as you have a reasonably plausible story about how you’ll get there.

(Investors are also not immune to a nice story. Customers are also not immune to a nice story. You can take this farther than you might think.)

So, unlike the re-trainers, you survive. And some of the time, you make it work. Your hammer-based screwdriving ends up morphing into something that, some of the time, actually does something the screwdrivers can’t. Instead of delusionally imagining nails, you’ve added a real ersatz nail to the world, where previously there was just a screw.

Making nails is a better path for you. Is it a better path for the world? I’m not sure.

If all those grants you won, all those jobs you and your students got, all that money from investors or customers drawn in by a good story, if that all went to the people who had the screwdrivers in the first place, could they have done a better job?

Sometimes, no. Sometimes you happen upon some real irreproducible magic. Your hammer is Thor’s hammer, and when hefted by the worthy it can do great things.

Sometimes, though, your hammer was just the hammer that got the funding. Now every screwdriver kit has to have a space for a little hammer, when it could have had another specialized screwdriver that fit better in the box.

In the end, the world is build out of these kinds of ill-fitting toolkits. We all try to survive, both as human beings and by our sub-culture’s concept of the good life. We each have our hammers, and regardless of whether the world is full of screws, we have to convince people they want a hammer anyway. Everything we do is built on a vast rickety pile of consequences, the end-results of billions of people desperate to be wanted. For those of us who love clean solutions and ideal paths, this is maddening and frustrating and terrifying. But it’s life, and in a world where we never know the ideal path, screw-nails and nail-screws are the best way we’ve found to get things done.