# At a Pedagogy Course

I’m at a pedagogy course this week. It’s the first time I’ve taken a course like this, and it has been really interesting learning about different approaches to teaching (which, as I keep being reminded, is very different from outreach!). It’s also really time-consuming: seven hours of class a day, with readings and lecture prep in the evening. As such, I haven’t had time to do a full blog post. Next week I’ll likely post some reflections about the course. Until then, here’s a slide from the practice lecture I gave:

# Electromagnetism Is the Weirdest Force

For a long time, physicists only knew about two fundamental forces: electromagnetism, and gravity. Physics students follow the same path, studying Newtonian gravity, then E&M, and only later learning about the other fundamental forces. If you’ve just recently heard about the weak nuclear force and the strong nuclear force, it can be tempting to think of them as just slight tweaks on electromagnetism. But while that can be a helpful way to start, in a way it’s precisely backwards. Electromagnetism is simpler than the other forces, that’s true. But because of that simplicity, it’s actually pretty weird as a force.

The weirdness of electromagnetism boils down to one key reason: the electromagnetic field has no charge.

Maybe that sounds weird to you: if you’ve done anything with electromagnetism, you’ve certainly seen charges. But while you’ve calculated the field produced by a charge, the field itself has no charge. You can specify the positions of some electrons and not have to worry that the electric field will introduce new charges you didn’t plan. Mathematically, this means your equations are linear in the field, and thus not all that hard to solve.

The other forces are different. The strong nuclear force has three types of charge, dubbed red, green, and blue. Not just quarks, but the field itself has charges under this system, making the equations that describe it non-linear.

Those properties mean that you can’t just think of the strong force as a push or pull between charges, like you could with electromagnetism. The strong force doesn’t just move quarks around, it can change their color, exchanging charge between the quark and the field. That’s one reason why when we’re more careful we refer to it as not the strong force, but the strong interaction.

The weak force also makes more sense when thought of as an interaction. It can change even more properties of particles, turning different flavors of quarks and leptons into each other, resulting in among other phenomena nuclear beta decay. It would be even more like the strong force, but the Higgs field screws that up, stirring together two more fundamental forces and spitting out the weak force and electromagnetism. The result ties them together in weird ways: for example, it means that the weak field can actually have an electric charge.

Interactions like the strong and weak forces are much more “normal” for particle physicists: if you ask us to picture a random fundamental force, chances are it will look like them. It won’t typically look like electromagnetism, the weird “degenerate” case with a field that doesn’t even have a charge. So despite how familiar electromagnetism may be to you, don’t take it as your model of what a fundamental force should look like: of all the forces, it’s the simplest and weirdest.

# Building One’s Technology

There are theoretical physicists who can do everything they do with a pencil and a piece of paper. I’m not one of them. The calculations I do are long, complicated, or tedious enough that they’re often best done with a computer. For a calculation like that, I can’t just use existing software “out of the box”: I need to program special-purpose tools to do the kind of calculation I need. This means each project has its own kind of learning curve. If I already have the right code, or almost the right code, things go very smoothly: with a few tweaks I can do a lot of interesting calculations. If I don’t have the right code yet, things go much more slowly: I have to build up my technology, figuring out what I need piece by piece until I’m back up to my usual speed.

I don’t always need to use computers to do my calculations. Sometimes my work hinges on something more conceptual: understanding a mathematical proof, or the arguments from another physicist’s paper. While this seems different on the surface, I’ve found that it has the same kinds of learning curves. If I know the right papers and mathematical methods, I can go pretty quickly. If I don’t, I have to “build up my technology”, reading and practicing, a slow build-up to my goal.

The times when I have to “build my technology” are always a bit frustrating. I don’t work as fast as I’d like, and I get tripped up by dumb mistakes. I keep having to go back, almost to the beginning, realizing that some aspect of how I set things up needs to be changed to make the rest work. As I go, though, the work gets more and more satisfying. I find pieces (of the code, of my understanding) that become solid, that I can rely on. I build my technology, and I can do more and more, and feel better about myself in the bargain. Eventually, I get back up to my full abilities, my technology set up, and a wide variety of calculations become possible.

# Doing Difficult Things Is Its Own Reward

Does antimatter fall up, or down?

Technically, we don’t know yet. The ALPHA-g experiment would have been the first to check this, making anti-hydrogen by trapping anti-protons and positrons in a long tube and seeing which way it falls. While they got most of their setup working, the LHC complex shut down before they could finish. It starts up again next month, so we should have our answer soon.

That said, for most theorists’ purposes, we absolutely do know: antimatter falls down. Antimatter is one of the cleanest examples of a prediction from pure theory that was confirmed by experiment. When Paul Dirac first tried to write down an equation that described electrons, he found the math forced him to add another particle with the opposite charge. With no such particle in sight, he speculated it could be the proton (this doesn’t work, they need the same mass), before Carl D. Anderson discovered the positron in 1932.

The same math that forced Dirac to add antimatter also tells us which way it falls. There’s a bit more involved, in the form of general relativity, but the recipe is pretty simple: we know how to take an equation like Dirac’s and add gravity to it, and we have enough practice doing it in different situations that we’re pretty sure it’s the right way to go. Pretty sure doesn’t mean 100% sure: talk to the right theorists, and you’ll probably find a proposal or two in which antimatter falls up instead of down. But they tend to be pretty weird proposals, from pretty weird theorists.

Ok, but if those theorists are that “weird”, that outside the mainstream, why does an experiment like ALPHA-g exist? Why does it happen at CERN, one of the flagship facilities for all of mainstream particle physics?

This gets at a misconception I occasionally hear from critics of the physics mainstream. They worry about groupthink among mainstream theorists, the physics community dismissing good ideas just because they’re not trendy (you may think I did that just now, for antigravity antimatter!) They expect this to result in a self-fulfilling prophecy where nobody tests ideas outside the mainstream, so they find no evidence for them, so they keep dismissing them.

The mistake of these critics is in assuming that what gets tested has anything to do with what theorists think is reasonable.

Theorists talk to experimentalists, sure. We motivate them, give them ideas and justification. But ultimately, people do experiments because they can do experiments. I watched a talk about the ALPHA experiment recently, and one thing that struck me was how so many different techniques play into it. They make antiprotons using a proton beam from the accelerator, slow them down with magnetic fields, and cool them with lasers. They trap their antihydrogen in an extremely precise vacuum, and confirm it’s there with particle detectors. The whole setup is a blend of cutting-edge accelerator physics and cutting-edge tricks for manipulating atoms. At its heart, ALPHA-g feels like its primary goal is to stress-test all of those tricks: to push the state of the art in a dozen experimental techniques in order to accomplish something remarkable.

And so even if the mainstream theorists don’t care, ALPHA will keep going. It will keep getting funding, it will keep getting visited by celebrities and inspiring pop fiction. Because enough people recognize that doing something difficult can be its own reward.

In my experience, this motivation applies to theorists too. Plenty of us will dismiss this or that proposal as unlikely or impossible. But give us a concrete calculation, something that lets us use one of our flashy theoretical techniques, and the tune changes. If we’re getting the chance to develop our tools, and get a paper out of it in the process, then sure, we’ll check your wacky claim. Why not?

I suspect critics of the mainstream would have a lot more success with this kind of pitch-based approach. If you can find a theorist who already has the right method, who’s developing and extending it and looking for interesting applications, then make your pitch: tell them how they can answer your question just by doing what they do best. They’ll think of it as a chance to disprove you, and you should let them, that’s the right attitude to take as a scientist anyway. It’ll work a lot better than accusing them of hogging the grant money.

# Theoretical Uncertainty and Uncertain Theory

Yesterday, Fermilab’s Muon g-2 experiment announced a new measurement of the magnetic moment of the muon, a number which describes how muons interact with magnetic fields. For what might seem like a small technical detail, physicists have been very excited about this measurement because it’s a small technical detail that the Standard Model seems to get wrong, making it a potential hint of new undiscovered particles. Quanta magazine has a great piece on the announcement, which explains more than I will here, but the upshot is that there are two different calculations on the market that attempt to predict the magnetic moment of the muon. One of them, using older methods, disagrees with the experiment. The other, with a new approach, agrees. The question then becomes, which calculation was wrong? And why?

What does it mean for a prediction to match an experimental result? The simple, wrong, answer is that the numbers must be equal: if you predict “3”, the experiment has to measure “3”. The reason why this is wrong is that in practice, every experiment and every prediction has some uncertainty. If you’ve taken a college physics class, you’ve run into this kind of uncertainty in one of its simplest forms, measurement uncertainty. Measure with a ruler, and you can only confidently measure down to the smallest divisions on the ruler. If you measure 3cm, but your ruler has ticks only down to a millimeter, then what you’re measuring might be as large as 3.1cm or as small as 2.9 cm. You just don’t know.

This uncertainty doesn’t mean you throw up your hands and give up. Instead, you estimate the effect it can have. You report, not a measurement of 3cm, but of 3cm plus or minus 1mm. If the prediction was 2.9cm, then you’re fine: it falls within your measurement uncertainty.

Measurements aren’t the only thing that can be uncertain. Predictions have uncertainty too, theoretical uncertainty. Sometimes, this comes from uncertainty on a previous measurement: if you make a prediction based on that experiment that measured 3cm plus or minus 1mm, you have to take that plus or minus into account and estimate its effect (we call this propagation of errors). Sometimes, the uncertainty comes instead from an approximation you’re making. In particle physics, we sometimes approximate interactions between different particles with diagrams, beginning with the simplest diagrams and adding on more complicated ones as we go. To estimate the uncertainty there, we estimate the size of the diagrams we left out, the more complicated ones we haven’t calculated yet. Other times, that approximation doesn’t work, and we need to use a different approximation, treating space and time as a finite grid where we can do computer simulations. In that case, you can estimate your uncertainty based on how small you made your grid. The new approach to predicting the muon magnetic moment uses that kind of approximation.

There’s a common thread in all of these uncertainty estimates: you don’t expect to be too far off on average. Your measurements won’t be perfect, but they won’t all be screwed up in the same way either: chances are, they will randomly be a little below or a little above the truth. Your calculations are similar: whether you’re ignoring complicated particle physics diagrams or the spacing in a simulated grid, you can treat the difference as something small and random. That randomness means you can use statistics to talk about your errors: you have statistical uncertainty. When you have statistical uncertainty, you can estimate, not just how far off you might get, but how likely it is you ended up that far off. In particle physics, we have very strict standards for this kind of thing: to call something new a discovery, we demand that it is so unlikely that it would only show up randomly under the old theory roughly one in a million times. The muon magnetic moment isn’t quite up to our standards for a discovery yet, but the new measurement brought it closer.

The two dueling predictions for the muon’s magnetic moment both estimate some amount of statistical uncertainty. It’s possible that the two calculations just disagree due to chance, and that better measurements or a tighter simulation grid would make them agree. Given their estimates, though, that’s unlikely. That takes us from the realm of theoretical uncertainty, and into uncertainty about the theoretical. The two calculations use very different approaches. The new calculation tries to compute things from first principles, using the Standard Model directly. The risk is that such a calculation needs to make assumptions, ignoring some effects that are too difficult to calculate, and one of those assumptions may be wrong. The older calculation is based more on experimental results, using different experiments to estimate effects that are hard to calculate but that should be similar between different situations. The risk is that the situations may be less similar than expected, their assumptions breaking down in a way that the bottom-up calculation could catch.

None of these risks are easy to estimate. They’re “unknown unknowns”, or rather, “uncertain uncertainties”. And until some of them are resolved, it won’t be clear whether Fermilab’s new measurement is a sign of undiscovered particles, or just a (challenging!) confirmation of the Standard Model.

# Is Outreach for Everyone?

Betteridge’s law applies here: the answer is “no”. It’s a subtle “no”, though.

As a scientist, you will always need to be able to communicate your work. Most of the time you can get away with papers and talks aimed at your peers. But the longer you mean to stick around, the more often you will have to justify yourself to others: to departments, to universities, and to grant agencies. A scientist cannot survive on scientific ability alone: to get jobs, to get funding, to survive, you need to be able to promote yourself, at least a little.

Self-promotion isn’t outreach, though. Talking to the public, or to journalists, is a different skill from talking to other academics or writing grants. And it’s entirely possible to go through an entire scientific career without exercising that skill.

That’s a reassuring message for some. I’ve met people for whom science is a refuge from the mess of human interaction, people horrified by the thought of fame or even being mentioned in a newspaper. When I meet these people, they sometimes seem to worry that I’m silently judging them, thinking that they’re ignoring their responsibilities by avoiding outreach. They think this in part because the field seems to be going in that direction. Grants that used to focus just on science have added outreach as a requirement, demanding that each application come with a plan for some outreach project.

I can’t guarantee that more grants won’t add outreach requirements. But I can say at least that I’m on your side here: I don’t think you should have to do outreach if you don’t want to. I don’t think you have to, just yet. And I think if grant agencies are sensible, they’ll find a way to encourage outreach without making it mandatory.

I think that overall, collectively, we have a responsibility to do outreach. Beyond the old arguments about justifying ourselves to taxpayers, we also just ought to be open about what we do. In a world where people are actively curious about us, we ought to encourage and nurture that curiosity. I don’t think this is unique to science, I think it’s something every industry, every hobby, and every community should foster. But in each case, I think that communication should be done by people who want to do it, not forced on every member.

I also think that, potentially, anyone can do outreach. Outreach can take different forms for different people, anything from speaking to high school students to talking to journalists to writing answers for Stack Exchange. I don’t think anyone should feel afraid of outreach because they think they won’t be good enough. Chances are, you know something other people don’t: I guarantee if you want to, you will have something worth saying.

# Redefining Fields for Fun and Profit

When we study subatomic particles, particle physicists use a theory called Quantum Field Theory. But what is a quantum field?

Some people will describe a field in vague terms, and say it’s like a fluid that fills all of space, or a vibrating rubber sheet. These are all metaphors, and while they can be helpful, they can also be confusing. So let me avoid metaphors, and say something that may be just as confusing: a field is the answer to a question.

Suppose you’re interested in a particle, like an electron. There is an electron field that tells you, at each point, your chance of detecting one of those particles spinning in a particular way. Suppose you’re trying to measure a force, say electricity or magnetism. There is an electromagnetic field that tells you, at each point, what force you will measure.

Sometimes the question you’re asking has a very simple answer: just a single number, for each point and each time. An example of a question like that is the temperature: pick a city, pick a date, and the temperature there and then is just a number. In particle physics, the Higgs field answers a question like that: at each point, and each time, how “Higgs-y” is it there and then? You might have heard that the Higgs field gives other particles their mass: what this means is that the more “Higgs-y” it is somewhere, the higher these particles’ mass will be. The Higgs field is almost constant, because it’s very difficult to get it to change. That’s in some sense what the Large Hadron Collider did when they discovered the Higgs boson: pushed hard enough to cause a tiny, short-lived ripple in the Higgs field, a small area that was briefly more “Higgs-y” than average.

We like to think of some fields as fundamental, and others as composite. A proton is composite: it’s made up of quarks and gluons. Quarks and gluons, as far as we know, are fundamental: they’re not made up of anything else. More generally, since we’re thinking about fields as answers to questions, we can just as well ask more complicated, “composite” questions. For example, instead of “what is the temperature?”, we can ask “what is the temperature squared?” or “what is the temperature times the Higgs-y-ness?”.

But this raises a troubling point. When we single out a specific field, like the Higgs field, why are we sure that that field is the fundamental one? Why didn’t we start with “Higgs squared” instead? Or “Higgs plus Higgs squared”? Or something even weirder?

That kind of swap, from Higgs to Higgs squared, is called a field redefinition. In the math of quantum field theory, it’s something you’re perfectly allowed to do. Sometimes, it’s even a good idea. Other times, it can make your life quite complicated.

The reason why is that some fields are much simpler than others. Some are what we call free fields. Free fields don’t interact with anything else. They just move, rippling along in easy-to-calculate waves.

Redefine a free field, swapping it for some more complicated function, and you can easily screw up, and make it into an interacting field. An interacting field might interact with another field, like how electromagnetic fields move (and are moved by) electrons. It might also just interact with itself, a kind of feedback effect that makes any calculation we’d like to do much more difficult.

If we persevere with this perverse choice, and do the calculation anyway, we find a surprise. The final results we calculate, the real measurements people can do, are the same in both theories. The field redefinition changed how the theory appeared, quite dramatically…but it didn’t change the physics.

You might think the moral of the story is that you must always choose the right fundamental field. You might want to, but you can’t: not every field is secretly free. Some will be interacting fields, whatever you do. In that case, you can make one choice or another to simplify your life…but you can also just refuse to make a choice.

That’s something quite a few physicists do. Instead of looking at a theory and calling some fields fundamental and others composite, they treat every one of these fields, every different question they could ask, on the same footing. They then ask, for these fields, what one can measure about them. They can ask which fields travel at the speed of light, and which ones go slower, or which fields interact with which other fields, and how much. Field redefinitions will shuffle the fields around, but the patterns in the measurements will remain. So those, and not the fields, can be used to specify the theory. Instead of describing the world in terms of a few fundamental fields, they think about the world as a kind of field soup, characterized by how it shifts when you stir it with a spoon.

It’s not a perspective everyone takes. If you overhear physicists, sometimes they will talk about a theory with only a few fields, sometimes they will talk about many, and you might be hard-pressed to tell what they’re talking about. But if you keep in mind these two perspectives: either a few fundamental fields, or a “field soup”, you’ll understand them a little better.

# Black Holes, Neutron Stars, and the Power of Love

What’s the difference between a black hole and a neutron star?

When a massive star nears the end of its life, it starts running out of nuclear fuel. Without the support of a continuous explosion, the star begins to collapse, crushed under its own weight.

What happens then depends on how much weight that is. The most massive stars collapse completely, into the densest form anything can take: a black hole. Einstein’s equations say a black hole is a single point, infinitely dense: get close enough and nothing, not even light, can escape. A quantum theory of gravity would change this, but not a lot: a quantum black hole would still be as dense as quantum matter can get, still equipped with a similar “point of no return”.

A slightly less massive star collapses, not to a black hole, but to a neutron star. Matter in a neutron star doesn’t collapse to a single point, but it does change dramatically. Each electron in the old star is crushed together with a proton until it becomes a neutron, a forced reversal of the more familiar process of Beta decay. Instead of a ball of hydrogen and helium, the star then ends up like a single atomic nucleus, one roughly the size of a city.

Now, let me ask a slightly different question: how do you tell the difference between a black hole and a neutron star?

Sometimes, you can tell this through ordinary astronomy. Neutron stars do emit light, unlike black holes, though for most neutron stars this is hard to detect. In the past, astronomers would use other objects instead, looking at light from matter falling in, orbiting, or passing by a black hole or neutron star to estimate its mass and size.

Now they have another tool: gravitational wave telescopes. Maybe you’ve heard of LIGO, or its European cousin Virgo: massive machines that do astronomy not with light but by detecting ripples in space and time. In the future, these will be joined by an even bigger setup in space, called LISA. When two black holes or neutron stars collide they “ring” the fabric of space and time like a bell, sending out waves in every direction. By analyzing the frequency of these waves, scientists can learn something about what made them: in particular, whether the waves were made by black holes or neutron stars.

One big difference between black holes and neutron stars lies in something called their “Love numbers“. From far enough away, you can pretend both black holes and neutron stars are single points, like fundamental particles. Try to get more precise, and this picture starts to fail, but if you’re smart you can include small corrections and keep things working. Some of those corrections, called Love numbers, measure how much one object gets squeezed and stretched by the other’s gravitational field. They’re called Love numbers not because they measure how hug-able a neutron star is, but after the mathematician who first proposed them, A. E. H. Love.

What can we learn from Love numbers? Quite a lot. More impressively, there are several different types of questions Love numbers can answer. There are questions about our theories, questions about the natural world, and questions about fundamental physics.

You might have heard that black holes “have no hair”. A black hole in space can be described by just two numbers: its mass, and how much it spins. A star is much more complicated, with sunspots and solar flares and layers of different gases in different amounts. For a black hole, all of that is compressed down to nothing, reduced to just those two numbers and nothing else.

With that in mind, you might think a black hole should have zero Love numbers: it should be impossible to squeeze it or stretch it. This is fundamentally a question about a theory, Einstein’s theory of relativity. If we took that theory for granted, and didn’t add anything to it, what would the consequences be? Would black holes have zero Love number, or not?

It turns out black holes do have zero Love number, if they aren’t spinning. If they are, things are more complicated: a few calculations made it look like spinning black holes also had zero Love number, but just last year a more detailed proof showed that this doesn’t hold. Somehow, despite having “no hair”, you can actually “squeeze” a spinning black hole.

(EDIT: Folks on twitter pointed out a wrinkle here: more recent papers are arguing that spinning black holes actually do have zero Love number as well, and that the earlier papers confused Love numbers with a different effect. All that is to say this is still very much an active area of research!)

The physics behind neutron stars is in principle known, but in practice hard to understand. When they are formed, almost every type of physics gets involved: gas and dust, neutrino blasts, nuclear physics, and general relativity holding it all together.

Because of all this complexity, the structure of neutron stars can’t be calculated from “first principles” alone. Finding it out isn’t a question about our theories, but a question about the natural world. We need to go out and measure how neutron stars actually behave.

Love numbers are a promising way to do that. Love numbers tell you how an object gets squeezed and stretched in a gravitational field. Learning the Love numbers of neutron stars will tell us something about their structure: namely, how squeezable and stretchable they are. Already, LIGO and Virgo have given us some information about this, and ruled out a few possibilities. In future, the LISA telescope will show much more.

Returning to black holes, you might wonder what happens if we don’t stick to Einstein’s theory of relativity. Physicists expect that relativity has to be modified to account for quantum effects, to make a true theory of quantum gravity. We don’t quite know how to do that yet, but there are a few proposals on the table.

Asking for the true theory of quantum gravity isn’t just a question about some specific part of the natural world, it’s a question about the fundamental laws of physics. Can Love numbers help us answer it?

Maybe. Some theorists think that quantum gravity will change the Love numbers of black holes. Fewer, but still some, think they will change enough to be detectable, with future gravitational wave telescopes like LISA. I get the impression this is controversial, both because of the different proposals involved and the approximations used to understand them. Still, it’s fun that Love numbers can answer so many different types of questions, and teach us so many different things about physics.

Unrelated: For those curious about what I look/sound like, I recently gave a talk of outreach advice for the Max Planck Institute for Physics, and they posted it online here.

# “Inreach”

This is, first and foremost, an outreach blog. I try to make my writing as accessible as possible, so that anyone from high school students to my grandparents can learn something. My goal is to get the general public to know a bit more about physics, and about the people who do it, both to better understand the world and to view us in a better light.

However, as I am occasionally reminded, my readers aren’t exactly the general public. I’ve done polls, and over 60% of you either have a PhD in physics, or are on your way to one. The rest include people with what one might call an unusually strong interest in physics: engineers with a fondness for the (2,0) theory, or retired lawyers who like to debate dark matter.

With that in mind, am I really doing outreach? Or am I doing some sort of “inreach” instead?

First, it’s important to remember that just because someone is a physicist doesn’t mean they’re an expert in everything. This is especially relevant when I talk about my own sub-field, but it matters for other topics too: experts in one part of physics can still find something to learn, and it’s still worth getting on their good side. Still, if that was my main audience, I’d probably want to strike a different tone, more like the colloquium talks we give for our fellow physicists.

Second, I like to think that outreach “trickles down”. I write for a general audience, and get read by “physics fans”, but they will go on to talk about physics to anyone who will listen: to parents who want to understand what they do, to people they’re trying to impress at parties, to friends they share articles with. If I write good metaphors and clear analogies, they will get passed on to those friends and parents, and the “inreach” will become outreach. I know that’s why I read other physicists’ outreach blogs: I’m looking for new tricks to make ideas clearer.

Third, active readers are not all readers. The people who answer a poll are more likely to be regulars, people who come back to the blog again and again, and those people are pretty obviously interested in physics. (Interested doesn’t mean expert, of course…but in practice, far more non-experts read blogs on, say, military history, than on physics.) But I suspect most of my readers aren’t regulars. My most popular post, “The Way You Think Everything Is Connected Isn’t the Way Everything Is Connected”, gets a trickle of new views every day. WordPress lets me see some of the search terms people use to find it, and there are people who literally google “is everything connected?” These aren’t physics PhDs looking for content, these are members of the general public who hear something strange and confusing and want to check it out. Being that check, the source someone googles to clear things up, that’s an honor. Knowing I’m serving that role, I know I’m not doing “just inreach”: I’m reaching out too.

# Reality as an Algebra of Observables

Listen to a physicist talk about quantum mechanics, and you’ll hear the word “observable”. Observables are, intuitively enough, things that can be observed. They’re properties that, in principle, one could measure in an experiment, like the position of a particle or its momentum. They’re the kinds of things linked by uncertainty principles, where the better you know one, the worse you know the other.

Some physicists get frustrated by this focus on measurements alone. They think we ought to treat quantum mechanics, not like a black box that produces results, but as information about some underlying reality. Instead of just observables, they want us to look for “beables“: not just things that can be observed, but things that something can be. From their perspective, the way other physicists focus on observables feels like giving up, like those physicists are abandoning their sacred duty to understand the world. Others, like the Quantum Bayesians or QBists, disagree, arguing that quantum mechanics really is, and ought to be, a theory of how individuals get evidence about the world.

I’m not really going to weigh in on that debate, I still don’t feel like I know enough to even write a decent summary. But I do think that one of the instincts on the “beables” side is wrong. If we focus on observables in quantum mechanics, I don’t think we’re doing anything all that unusual. Even in other parts of physics, we can think about reality purely in terms of observations. Doing so isn’t a dereliction of duty: often, it’s the most useful way to understand the world.

When we try to comprehend the world, we always start alone. From our time in the womb, we have only our senses and emotions to go on. With a combination of instinct and inference we start assembling a consistent picture of reality. Philosophers called phenomenologists (not to be confused with the physicists called phenomenologists) study this process in detail, trying to characterize how different things present themselves to an individual consciousness.

For my point here, these details don’t matter so much. That’s because in practice, we aren’t alone in understanding the world. Based on what others say about the world, we conclude they perceive much like we do, and we learn by their observations just as we learn by our own. We can make things abstract: instead of the specifics of how individuals perceive, we think about groups of scientists making measurements. At the end of this train lie observables: things that we as a community could in principle learn, and share with each other, ignoring the details of how exactly we measure them.

If each of these observables was unrelated, just scattered points of data, then we couldn’t learn much. Luckily, they are related. In quantum mechanics, some of these relationships are the uncertainty principles I mentioned earlier. Others relate measurements at different places, or at different times. The fancy way to refer to all these relationships is as an algebra: loosely, it’s something you can “do algebra with”, like you did with numbers and variables in high school. When physicists and mathematicians want to do quantum mechanics or quantum field theory seriously, they often talk about an “algebra of observables”, a formal way of thinking about all of these relationships.

Focusing on those two things, observables and how they are related, isn’t just useful in the quantum world. It’s an important way to think in other areas of physics too. If you’ve heard people talk about relativity, the focus on measurement screams out, in thought experiments full of abstract clocks and abstract yardsticks. Without this discipline, you find paradoxes, only to resolve them when you carefully track what each person can observe. More recently, physicists in my field have had success computing the chance particles collide by focusing on the end result, the actual measurements people can make, ignoring what might happen in between to cause that measurement. We can then break measurements down into simpler measurements, or use the structure of simpler measurements to guess more complicated ones. While we typically have done this in quantum theories, that’s not really a limitation: the same techniques make sense for problems in classical physics, like computing the gravitational waves emitted by colliding black holes.

With this in mind, we really can think of reality in those terms: not as a set of beable objects, but as a set of observable facts, linked together in an algebra of observables. Paring things down to what we can know in this way is more honest, and it’s also more powerful and useful. Far from a betrayal of physics, it’s the best advantage we physicists have in our quest to understand the world.