Some of the particles of the Standard Model are more familiar than others. Electrons and photons, of course, everyone has heard of, and most, though not all, have heard of quarks. Many of the rest, like the W and Z boson, only appear briefly in high-energy colliders. But one Standard Model particle is much less exotic, and nevertheless leads to all manner of confusion. That particle is the neutrino.
Neutrinos are very light, much lighter than even an electron. (Until relatively recently, we thought they were completely massless!) They have no electric charge and they don’t respond to the strong nuclear force, so aside from gravity (negligible since they’re so light), the only force that affects them is the weak nuclear force. This force is, well, weak. It means neutrinos can be produced via the relatively ordinary process of radioactive beta decay, but it also means they almost never interact with anything else. Vast numbers of neutrinos pass through you every moment, with no noticeable effect. We need enormous tanks of liquid or chunks of ice to have a chance of catching neutrinos in action.
Because neutrinos are both ordinary and unfamiliar, they tend to confuse people. I’d like to take advantage of this confusion to teach some physics. Neutrinos turn out to be a handy theme to convey a couple blog posts worth of lessons about why physics works the way it does.
I’ll start on the historical side. There’s a lesson that physicists themselves learned in the early days:
Lesson 1: Don’t Throw out a Well-Justified Conservation Law
In the early 20th century, physicists were just beginning to understand radioactivity. They could tell there were a few different types: gamma decay released photons in the form of gamma rays, alpha decay shot out heavy, positively charged particles, and beta decay made “beta particles”, or electrons. For each of these, physicists could track each particle and measure its energy and momentum. Everything made sense for gamma and alpha decay…but not for beta decay. Somehow, they could add up the energy of each of the particles they could track, and find less at the end than they did at the beginning. It was as if energy was not conserved.
These were the heady early days of quantum mechanics, so people were confused enough that many thought this was the end of the story. Maybe energy just isn’t conserved? Wolfgang Pauli, though, thought differently. He proposed that there had to be another particle, one that no-one could detect, that made energy balance out. It had to be neutral, so he called it the neutron…until two years later when James Chadwick discovered the particle we call the neutron. This was much too heavy to be Pauli’s neutron, so Edoardo Amaldi joked that Pauli’s particle was a “neutrino” instead. The name stuck, and Pauli kept insisting his neutrino would turn up somewhere. It wasn’t until 1956 that neutrinos were finally detected, so for quite a while people made fun of Pauli for his quixotic quest.
As we came to our more modern understanding, physicists started writing up the Standard Model. Neutrinos were thought of as massless, like photons, traveling at the speed of light. Now, we know that neutrinos have mass…but we don’t know how much mass they have. How do we know they have mass then? To understand that, you’ll need to understand what mass actually means in physics. We’ll talk about that next week!
In my line of work, I spend a lot of time explaining physics. I write posts here of course, and give the occasional public lecture. I also explain physics when I supervise Master’s students, and in a broader sense whenever I chat with my collaborators or write papers. I’ll explain physics even more when I start teaching. But of all the ways to explain physics, there’s one that has always been my favorite: the one-on-one conversation.
Talking science one-on-one is validating in a uniquely satisfying way. You get instant feedback, questions when you’re unclear and comprehension when you’re close. There’s a kind of puzzle to it, discovering what you need to fill in the gaps in one particular person’s understanding. As a kid, I’d chase this feeling with imaginary conversations: I’d plot out a chat with Democritus or Newton, trying to explain physics or evolution or democracy. It was a game, seeing how I could ground our modern understanding in concepts someone from history already knew.
I’ll never get a chance in real life to explain physics to a Democritus or a Newton, to bridge a gap quite that large. But, as I’ve discovered over the years, everyone has bits and pieces they don’t yet understand. Even focused on the most popular topics, like black holes or elementary particles, everyone has gaps in what they’ve managed to pick up. I do too! So any conversation can be its own kind of adventure, discovering what that one person knows, what they don’t, and how to connect the two.
Of course, there’s fun in writing and public speaking too (not to mention, of course, research). Still, I sometimes wonder if there’s a career out there in just the part I like best: just one conversation after another, delving deep into one person’s understanding, making real progress, then moving on to the next. It wouldn’t be efficient by any means, but it sure sounds fun.
When most people think of the Big Bang, they imagine a single moment: a whole universe emerging from nothing. That’s not really how it worked, though. The Big Bang refers not to one event, but to a whole scientific theory. Using Einstein’s equations and some simplifying assumptions, we physicists can lay out a timeline for the universe’s earliest history. Different parts of this timeline have different evidence: some are meticulously tested, others we even expect to be wrong! It’s worth talking through this timeline and discussing what we know about each piece, and how we know it.
We can see surprisingly far back in time. As we look out into the universe, we see each star as it was when the light we see left it: longer ago the further the star is from us. Looking back, we see changes in the types of stars and galaxies: stars formed without the metals that later stars produced, galaxies made of those early stars. We see the universe become denser and hotter, until eventually we reach the last thing we can see: the cosmic microwave background, a faint light that fills our view in every direction. This light represents a change in the universe, the emergence of the first atoms. Before this, there were ions: free nuclei and electrons, forming a hot plasma. That plasma constantly emitted and absorbed light. As the universe cooled, the ions merged into atoms, and light was free to travel. Because of this, we cannot see back beyond this point. Our model gives detailed predictions for this curtain of light: its temperature, and even the ways it varies in intensity from place to place, which in turn let us hone our model further.
In principle, we could “see” a bit further. Light isn’t the only thing that travels freely through the universe. Neutrinos are almost massless, and pass through almost everything. Like the cosmic microwave background, the universe should have a cosmic neutrino background. This would come from much earlier, from an era when the universe was so dense that neutrinos regularly interacted with other matter. We haven’t detected this neutrino background yet, but future experiments might. Gravitational waves meanwhile, can also pass through almost any obstacle. There should be gravitational wave backgrounds as well, from a variety of eras in the early universe. Once again these haven’t been detected yet, but more powerful gravitational wave telescopes may yet see them.
We have indirect evidence a bit further back than we can see things directly. In the heat of the early universe the first protons and neutrons were merged via nuclear fusion, becoming the first atomic nuclei: isotopes of hydrogen, helium, and lithium. Our model lets us predict the proportions of these, how much helium and lithium per hydrogen atom. We can then compare this to the oldest stars we see, and see that the proportions are right. In this way, we know something about the universe from before we can “see” it.
We get surprised when we look at the universe on large scales, and compare widely separated regions. We find those regions are surprisingly similar, more than we would expect from randomness and the physics we know. Physicists have proposed different explanations for this. The most popular, cosmic inflation, suggests that the universe expanded very rapidly, accelerating so that a small region of similar matter was blown up much larger than the ordinary Big Bang model would have, projecting those similarities across the sky. While many think this proposal fits the data best, we still aren’t sure it’s the right one: there are alternate proposals, and it’s even controversial whether we should be surprised by the large-scale similarity in the first place.
We understand, in principle, how matter can come from “nothing”. This is sometimes presented as the most mysterious part of the Big Bang, the idea that matter could spontaneously emerge from an “empty” universe. But to a physicist, this isn’t very mysterious. Matter isn’t actually conserved, mass is just energy you haven’t met yet. Deep down, the universe is just a bunch of rippling quantum fields, with different ones more or less active at different times. Space-time itself is just another field, the gravitational field. When people say that in the Big Bang matter emerged from nothing, all they mean is that energy moved from the gravitational field to fields like the electron and quark, giving rise to particles. As we wind the model back, we can pretty well understand how this could happen.
If we extrapolate, winding Einstein’s equations back all the way, we reach a singularity: the whole universe, according to those equations, would have emerged from a single point, a time when everything was zero distance from everything else. This assumes, though, that Einstein’s equations keep working all the way back that far. That’s probably wrong, though. Einstein’s equations don’t include the effect of quantum mechanics, which should be much more important when the universe is at its hottest and densest. We don’t have a complete theory of quantum gravity yet (at least, not one that can model this), so we can’t be certain how to correct these equations. But in general, quantum theories tend to “fuzz out” singularities, spreading out a single point over a wider area. So it’s likely that the universe didn’t actually come from just a single point, and our various incomplete theories of quantum gravity tend to back this up.
So, starting from what we can see, we extrapolate back to what we can’t. We’re quite confident in some parts of the Big Bang theory: the emergence of the first galaxies, the first stars, the first atoms, and the first elements. Back far enough and things get more mysterious, we have proposals but no definite answers. And if you try to wind back up to the beginning, you find we still don’t have the right kind of theory to answer the question. That’s a task for the future.
The scientific method, as we usually learn it, starts with a hypothesis. The scientist begins with a guess, and asks a question with a clear answer: true, or false? That guess lets them design an experiment, observe the consequences, and improve our knowledge of the world.
But where did the scientist get the hypothesis in the first place? Often, through some form of exploratory research.
Exploratory research is research done, not to answer a precise question, but to find interesting questions to ask. Each field has their own approach to exploration. A psychologist might start with interviews, asking broad questions to find narrower questions for a future survey. An ecologist might film an animal, looking for changes in its behavior. A chemist might measure many properties of a new material, seeing if any stand out. Each approach is like digging for treasure, not sure of exactly what you will find.
Mathematicians and theoretical physicists don’t do experiments, but we still need hypotheses. We need an idea of what we plan to prove, or what kind of theory we want to build: like other scientists, we want to ask a question with a clear, true/false answer. And to find those questions, we still do exploratory research.
What does exploratory research look like, in the theoretical world? Often, it begins with examples and calculations. We can start with a known method, or a guess at a new one, a recipe for doing some specific kind of calculation. Recipe in hand, we proceed to do the same kind of calculation for a few different examples, covering different sorts of situation. Along the way, we notice patterns: maybe the same steps happen over and over, or the result always has some feature.
We can then ask, do those same steps always happen? Does the result really always have that feature? We have our guess, our hypothesis, and our attempt to prove it is much like an experiment. If we find a proof, our hypothesis was true. On the other hand, we might not be able to find a proof. Instead, exploring, we might find a counterexample – one where the steps don’t occur, the feature doesn’t show up. That’s one way to learn that our hypothesis was false.
This kind of exploration is essential to discovery. As scientists, we all have to eventually ask clear yes/no questions, to submit our beliefs to clear tests. But we can’t start with those questions. We have to dig around first, to observe the world without a clear plan, to get to a point where we have a good question to ask.
A couple different things that some of you might like to know about:
Are you an amateur with an idea you think might revolutionize all of physics? If so, absolutely do not contact me about it. Instead, you can talk to these people. Sabine Hossenfelder runs a service that will hook you up with a scientist who will patiently listen to your idea and help you learn what you need to develop it further. They do charge for that service, and they aren’t cheap, so only do this if you can comfortably afford it. If you can’t, then I have some advice in a post here. Try to contact people who are experts in the specific topic you’re working on, ask concrete questions that you expect to give useful answers, and be prepared to do some background reading.
Are you an undergraduate student planning for a career in theoretical physics? If so, consider the Perimeter Scholars International (PSI) master’s program. Located at the Perimeter Institute in Waterloo, Canada, PSI is an intense one-year boot-camp in theoretical physics, teaching the foundational ideas you’ll need for the rest of your career. It’s something I wish I was aware of when I was applying for schools at that age. Theoretical physics is a hard field, and a big part of what makes it hard is all the background knowledge one needs to take part in it. Starting work on a PhD with that background knowledge already in place can be a tremendous advantage. There are other programs with similar concepts, but I’ve gotten a really good impression of PSI specifically so it’s them I would recommend. Note that applications for the new year aren’t open yet: I always plan to advertise them when they open, and I always forget. So consider this an extremely-early warning.
Are you an amplitudeologist? Registration for Amplitudes 2021 is now live! We’re doing an online conference this year, co-hosted by the Niels Bohr Institute and Penn State. We’ll be doing a virtual poster session, so if you want to contribute to that please include a title and abstract when you register. We also plan to stream on YouTube, and will have a fun online surprise closer to the conference date.
Why do particle physicists need those enormous colliders? Why does it take a big, expensive, atom-smashing machine to discover what happens on the smallest scales?
A machine like the Large Hadron Collider seems pretty complicated. But at its heart, it’s basically just a huge microscope.
If you’ve ever used a microscope in school, you probably had one with a light switch. Forget to turn on the light, and you spend a while confused about why you can’t see anything before you finally remember to flick the switch. Just like seeing something normally, seeing something with a microscope means that light is bouncing off that thing and hitting your eyes. Because of this, microscopes are limited by the wavelength of the light that they use. Try to look at something much smaller than that wavelength and the image will be too blurry to understand.
To see smaller details then, people use light with smaller wavelengths. Using massive X-ray producing machines called synchrotrons, scientists can study matter on the sub-nanometer scale. To go further, scientists can take advantage of wave-particle duality, and use electrons instead of light. The higher the energy of the electrons, the smaller their wavelength. The best electron microscopes can see objects measured in angstroms, not just nanometers.
A particle collider pushes this even further. The Large Hadron Collider accelerates protons until they have 6.5 Tera-electron-Volts of energy. That might be an unfamiliar type of unit, but if you’ve seen it before you can run the numbers, and estimate that this means the LHC can sees details below the attometer scale. That’s a quintillionth of a meter, or a hundred million times smaller than an atom.
A microscope isn’t just light, though, and a collider isn’t just high-energy protons. If it were, we could just wait and look at the sky. So-called cosmic rays are protons and other particles that travel to us from outer space. These can have very high energy: protons with similar energy to those in the LHC hit our atmosphere every day, and rays have been detected that were millions of times more powerful.
People sometimes ask why we can’t just use these cosmic rays to study particle physics. While we can certainly learn some things from cosmic rays, they have a big limitation. They have the “light” part of a microscope, but not the “lens”!
A microscope lens magnifies what you see. Starting from a tiny image, the lens blows it up until it’s big enough that you can see it with your own eyes. Particle colliders have similar technology, using their particle detectors. When two protons collider inside the LHC, they emit a flurry of other particles: photons and electrons, muons and mesons. Each of these particles is too small to see, let alone distinguish with the naked eye. But close to the collision there are detector machines that absorb these particles and magnify their signal. A single electron hitting one of these machines triggers a cascade of more and more electrons, in proportion to the energy of the electron that entered the machine. In the end, you get a strong electrical signal, which you can record with a computer. There are two big machines that do this at the Large Hadron Collider, each with its own independent scientific collaboration to run it. They’re called ATLAS and CMS.
So studying small scales needs two things: the right kind of “probe”, like light or protons, and a way to magnify the signal, like a lens or a particle detector. That’s hard to do without a big expensive machine…unless nature is unusually convenient. One interesting possibility is to try to learn about particle physics via astronomy. In the Big Bang particles collided with very high energy, and as the universe has expanded since then those details have been magnified across the sky. That kind of “cosmological collider” has the potential to teach us about physics at much smaller scales than any normal collider could reach. A downside is that, unlike in a collider, we can’t run the experiment over and over again: our “cosmological collider” only ran once. Still, if we want to learn about the very smallest scales, some day that may be our best option.
It’s a question famous for its sheer pointlessness. While probably no-one ever had that exact debate, “how many angels fit on a pin” has become a metaphor, first for a host of old theology debates that went nowhere, and later for any academic study that seems like a waste of time. Occasionally, physicists get accused of doing this: typically string theorists, but also people who debate interpretations of quantum mechanics.
Are those accusations fair? Sometimes yes, sometimes no. In order to tell the difference, we should think about what’s wrong, exactly, with counting angels on the head of a pin.
One obvious answer is that knowing the number of angels that fit on a needle’s point is useless. Wikipedia suggests that was the origin of the metaphor in the first place, a pun on “needle’s point” and “needless point”. But this answer is a little too simple, because this would still be a useful debate if angels were real and we could interact with them. “How many angels fit on the head of a pin” is really a question about whether angels take up space, whether two angels can be at the same place at the same time. Asking that question about particles led physicists to bosons and fermions, which among other things led us to invent the laser. If angelology worked, perhaps we would have angel lasers as well.
“If angelology worked” is key here, though. Angelology didn’t work, it didn’t lead to angel-based technology. And while Medieval people couldn’t have known that for certain, maybe they could have guessed. When people accuse academics of “counting angels on the head of a pin”, they’re saying they should be able to guess that their work is destined for uselessness.
How do you guess something like that?
Well, one problem with counting angels is that nobody doing the counting had ever seen an angel. Counting angels on the head of a pin implies debating something you can’t test or observe. That can steer you off-course pretty easily, into conclusions that are either useless or just plain wrong.
This can’t be the whole of the problem though, because of mathematics. We rarely accuse mathematicians of counting angels on the head of a pin, but the whole point of math is to proceed by pure logic, without an experiment in sight. Mathematical conclusions can sometimes be useless (though we can never be sure, some ideas are just ahead of their time), but we don’t expect them to be wrong.
The key difference is that mathematics has clear rules. When two mathematicians disagree, they can look at the details of their arguments, make sure every definition is as clear as possible, and discover which one made a mistake. Working this way, what they build is reliable. Even if it isn’t useful yet, the result is still true, and so may well be useful later.
In contrast, when you imagine Medieval monks debating angels, you probably don’t imagine them with clear rules. They might quote contradictory bible passages, argue everyday meanings of words, and win based more on who was poetic and authoritative than who really won the argument. Picturing a debate over how many angels can fit on the head of a pin, it seems more like Calvinball than like mathematics.
This then, is the heart of the accusation. Saying someone is just debating how many angels can dance on a pin isn’t merely saying they’re debating the invisible. It’s saying they’re debating in a way that won’t go anywhere, a debate without solid basis or reliable conclusions. It’s saying, not just that the debate is useless now, but that it will likely always be useless.
As an outsider, you can’t just dismiss a field because it can’t do experiments. What you can and should do, is dismiss a field that can’t produce reliable knowledge. This can be hard to judge, but a key sign is to look for these kinds of Calvinball-style debates. Do people in the field seem to argue the same things with each other, over and over? Or do they make progress and open up new questions? Do the people talking seem to be just the famous ones? Or are there cases of young and unknown researchers who happen upon something important enough to make an impact? Do people just list prior work in order to state their counter-arguments? Or do they build on it, finding consequences of others’ trusted conclusions?
A few corners of string theory do have this Calvinball feel, as do a few of the debates about the fundamentals of quantum mechanics. But if you look past the headlines and blogs, most of each of these fields seems more reliable. Rather than interminable back-and-forth about angels and pinheads, these fields are quietly accumulating results that, one way or another, will give people something to build on.
I’ve found that when it comes to reading papers, there are two distinct things I look for.
Sometimes, I read a paper looking for an answer. Typically, this is a “how to” kind of answer: I’m trying to do something, and the paper I’m reading is supposed to explain how. More rarely, I’m directly using a result: the paper proved a theorem or compute a formula, and I just take it as written and use it to calculate something else. Either way, I’m seeking out the paper with a specific goal in mind, which typically means I’m reading it long after it came out.
Other times, I read a paper looking for a question. Specifically, I look for the questions the author couldn’t answer. Sometimes these are things they point out, limitations of their result or opportunities for further study. Sometimes, these are things they don’t notice, holes or patterns in their results that make me wonder “what if?” Either can be the seed of a new line of research, a problem I can solve with a new project. If I read a paper in this way, typically it just came out, and this is the first time I’ve read it. When that isn’t the case, it’s because I start out with another reason to read it: often I’m looking for an answer, only to realize the answer I need isn’t there. The missing answer then becomes my new question.
I’m curious about the balance of these two behaviors in different fields. My guess is that some fields read papers more for their answers, while others read them more for their questions. If you’re working in another field, let me know what you do in the comments!
A reader pointed me to Stephen Wolfram’s one-year update of his proposal for a unified theory of physics. I was pretty squeamish about it one year ago, and now I’m even less interested in wading in to the topic. But I thought it would be worth saying something, and rather than say something specific, I realized I could say something general. I thought I’d talk a bit about how we judge good and bad research in theoretical physics.
In science, there are two things we want out of a new result: we want it to be true, and we want it to be surprising. The first condition should be obvious, but the second is also important. There’s no reason to do an experiment or calculation if it will just tell us something we already know. We do science in the hope of learning something new, and that means that the best results are the ones we didn’t expect.
(What about replications? We’ll get there.)
If you’re judging an experiment, you can measure both of these things with statistics. Statistics lets you estimate how likely an experiment’s conclusion is to be true: was there a large enough sample? Strong enough evidence? It also lets you judge how surprising the experiment is, by estimating how likely it would be to happen given what was known beforehand. Did existing theories and earlier experiments make the result seem likely, or unlikely? While you might not have considered replications surprising, from this perspective they can be: if a prior experiment seems unreliable, successfully replicating it can itself be a surprising result.
If instead you’re judging a theoretical result, these measures get more subtle. There aren’t always good statistical tools to test them. Nonetheless, you don’t have to rely on vague intuitions either. You can be fairly precise, both about how true a result is and how surprising it is.
We get our results in theoretical physics through mathematical methods. Sometimes, this is an actual mathematical proof: guaranteed to be true, no statistics needed. Sometimes, it resembles a proof, but falls short: vague definitions and unstated assumptions mar the argument, making it less likely to be true. Sometimes, the result uses an approximation. In those cases we do get to use some statistics, estimating how good the approximation may be. Finally, a result can’t be true if it contradicts something we already know. This could be a logical contradiction in the result itself, but if the result is meant to describe reality (note: not always the case), it might contradict the results of a prior experiment.
What makes a theoretical result surprising? And how precise can we be about that surprise?
Theoretical results can be surprising in the light of earlier theory. Sometimes, this gets made precise by a no-go theorem, a proof that some kind of theoretical result is impossible to obtain. If a result finds a loophole in a no-go theorem, that can be quite surprising. Other times, a result is surprising because it’s something no-one else was able to do. To be precise about that kind of surprise, you need to show that the result is something others wanted to do, but couldn’t. Maybe someone else made a conjecture, and only you were able to prove it. Maybe others did approximate calculations, and now you can do them more precisely. Maybe a question was controversial, with different people arguing for different sides, and you have a more conclusive argument. This is one of the better reasons to include a long list of references in a paper: not to pad your friends’ citation counts, but to show that your accomplishment is surprising: that others might have wanted to achieve it, but had to settle for something lesser.
In general, this means that showing whether a theoretical result is good: not merely true, but surprising and new, links you up to the rest of the theoretical community. You can put in all the work you like on a theory of everything, and make it as rigorous as possible, but if all you did was reproduce a sub-case of someone else’s theory then you haven’t accomplished all that much. If you put your work in context, compare and contrast to what others have done before, then we can start getting precise about how much we should be surprised, and get an idea of what your result is really worth.
When you look into your mirror in the morning, the face looking back at you isn’t exactly your own. Your mirror image is flipped: left-handed if you’re right-handed, and right-handed if you’re left-handed. Your body is not symmetric in the mirror: we say it does not respect parity symmetry. Zoom in, and many of the molecules in your body also have a “handedness” to them: biology is not the same when flipped in a mirror.
What about physics? At first, you might expect the laws of physics themselves to respect parity symmetry. Newton’s laws are the same when reflected in a mirror, and so are Maxwell’s. But one part of physics breaks this rule: the weak nuclear force, the force that causes nuclear beta decay. The weak nuclear force interacts differently with “right-handed” and “left-handed” particles (shorthand for particles that spin counterclockwise or clockwise with respect to their motion). This came as a surprise to most physicists, but it was predicted by Tsung-Dao Lee and Chen-Ning Yang and demonstrated in 1956 by Chien-Shiung Wu, known in her day as the “Queen of Nuclear Research”. The world really does look different when flipped in a mirror.
I gave a lecture on the weak force for the pedagogy course I took a few weeks back. One piece of feedback I got was that the topic wasn’t very relatable. People wanted to know why they should care about the handedness of the weak force, they wanted to hear about “real-life” applications. Once scientists learned that the weak force didn’t respect parity, what did that let us do?
Thinking about this, I realized this is actually a pretty tricky story to tell. With enough time and background, I could explain that the “handedness” of the Standard Model is a major constraint on attempts to unify physics, ruling out a lot of the simpler options. That’s hard to fit in a short lecture though, and it still isn’t especially close to “real life”.
Then I realized I don’t need to talk about “real life” to give a “real-life example”. People explaining relativity get away with science fiction scenarios, spaceships on voyages to black holes. The key isn’t to be familiar, just relatable. If I can tell a story (with people in it), then maybe I can make this work.
All I need, then, is a person who cares a lot about the world behind a mirror.
In order to make this story work, we have to get Alice to care about the weak nuclear force. The most familiar thing the weak force does is cause beta decay. And the most familiar thing that undergoes beta decay is a banana. Bananas contain radioactive potassium, which can transform to calcium by emitting an electron and an anti-electron-neutrino.
The radioactive potassium from a banana doesn’t stay in the body very long, only a few hours at most. But if Alice was especially paranoid about radioactivity, maybe she would want to avoid eating bananas. (We shouldn’t tell her that other foods contain potassium too.) If so, she might view the looking glass as a golden opportunity, a chance to eat as many bananas as she likes without worrying about radiation.
Does this work?
A first problem: can Alice even eat mirror-reversed bananas? I told you many biological molecules have handedness, which led Alan Moore’s version of Alice to starve. If we assume, unlike Moore, that Alice comes back in her original configuration and survives, we should still ask if she gets any benefit out of the bananas in the looking glass.
Researching this, I found that the main thing that makes bananas taste “banana-ish”, isoamyl acetate, does not have handedness: mirror bananas will still taste like bananas. Fructose, a sugar in bananas, does have handedness however: it isn’t the same when flipped in a mirror. Chatting with a chemist, the impression I got was that this isn’t a total loss: often, flipping a sugar results in another, different sugar. A mirror banana might still taste sweet, but less so. Overall, it may still be worth eating.
The next problem is a tougher one: flipping a potassium atom doesn’t actually make it immune to the weak force. The weak force only interacts with left-handed particles and right-handed antiparticles: in beta decay, it transforms a left-handed down quark to a left-handed up quark, producing a left-handed electron and a right-handed anti-neutrino.
Alice would have been fine if all of the quarks in potassium were left-handed, but they aren’t: an equal amount are right-handed, so the mirror weak force will still act on them, and they will still undergo beta decay. Actually, it’s worse than that: quarks, and massive particles in general, don’t actually have a definite handedness. If you speed up enough to catch up to a quark and pass it, then from your perspective it’s now going in the opposite direction, and its handedness is flipped. The only particles with definite handedness are massless particles: those go at the speed of light, so you can never catch up to them. Another way to think about this is that quarks get their mass from the Higgs field, and this happens because the Higgs lets left- and right-handed quarks interact. What we call the quark’s mass is in some sense just left- and right-handed quarks constantly mixing back and forth.
It turns out there’s a problem with even this scheme, though. The problem is a much wider one: the whole story is physically inconsistent.
I’d been acting like Alice can pass back and forth through the mirror, carrying all her particles with her. But what are “her particles”? If she carries a banana through the mirror, you might imagine the quarks in the potassium atoms carry over. But those quarks are constantly exchanging other quarks and gluons, as part of the strong force holding them together. They’re also exchanging photons with electrons via the electromagnetic force, and they’re also exchanging W bosons via beta decay. In quantum field theory, all of this is in some sense happening at once, an infinite sum over all possible exchanges. It doesn’t make sense to just carve out one set of particles and plug them in to different fields somewhere else.
If we actually wanted to describe a mirror like Alice’s looking glass in physics, we’d want to do it consistently. This is similar to how physicists think of time travel: you can’t go back in time and murder your grandparents because your whole path in space-time has to stay consistent. You can only go back and do things you “already did”. We treat space in a similar way to time. A mirror like Alice’s imposes a condition, that fields on one side are equal to their mirror image on the other side. Conditions like these get used in string theory on occasion, and they have broad implications for physics on the whole of space-time, not just near the boundary. The upshot is that a world with a mirror like Alice’s in it would be totally different from a world without the looking glass: the weak force as we know it would not exist.
So unfortunately, I still don’t have a good “real life” story for a class about parity symmetry. It’s fun trying to follow Alice through a parity transformation, but there are a few too many problems for the tale to make any real sense. Feel free to suggest improvements!