For overambitious apes like us, adding integers is the easiest thing in the world. Take one berry, add another, and you have two. Each remains separate, you can lay them in a row and count them one by one, each distinct thing adding up to a group of distinct things.
Other things in math are less like berries. Add two real numbers, like pi and the square root of two, and you get another real number, bigger than the first two, something you can write in an infinite messy decimal. You know in principle you can separate it out again (subtract pi, get the square root of two), but you can’t just stare at it and see the parts. This is less like adding berries, and more like adding fluids. Pour some water in to some other water, and you certainly have more water. You don’t have “two waters”, though, and you can’t tell which part started as which.
Some things in math look like berries, but are really like fluids. Take a polynomial, say . It looks like three types of things, like three berries: five , six , and eight . Add another polynomial, and the illusion continues: add and you get . You’ve just added more , more , more , like adding more strawberries, blueberries, and raspberries.
But those berries were a choice you made, and not the only one. You can rewrite that first polynomial, for example saying . That’s the same thing, you can check. But now it looks like five , negative four , and seven . It’s different numbers of different things, blackberries or gooseberries or something. And you can do this in many ways, infinitely many in fact. The polynomial isn’t really a collection of berries, for all it looked like one. It’s much more like a fluid, a big sloshing mess you can pour into buckets of different sizes. (Technically, it’s a vector space. Your berries were a basis.)
Even smart, advanced students can get tripped up on this. You can be used to treating polynomials as a fluid, and forget that directions in space are a fluid, one you can rotate as you please. If you’re used to directions in space, you’ll get tripped up by something else. You’ll find that types of particles can be more fluid than berry, the question of which quark is which not as simple as how many strawberries and blueberries you have. The laws of physics themselves are much more like a fluid, which should make sense if you take a moment, because they are made of equations, and equations are like a fluid.
So my fellow overambitious apes, do be careful. Not many things are like berries in the end. A whole lot are like fluids.
Monday is Valentine’s Day, so I’m following my yearly tradition and posting a poem about love and physics. If you like it, be sure to check out my poems from past years here.
A physicist once dreamed
of a life like a crystal.
Each facet the same, again and again,
until the end of time.
This is, of course, impossible.
A physicist once dreamed
of a life like a crystal.
Each facet the same, again and again,
with reliable effort
(what the young physicists call work).
This, (you might say of course,) is possible.
It means more than you’d think.
A thing we model as a spring
(or: anyone and anything)
has a restoring force:
a force to pull it back
a force to keep it going.
A thing we model as a spring
(yes you and me and everything)
has a damping force, too:
this slows it down
and tires it out.
The dismal law
of finite life.
The driving force is another thing
no mere possession of the spring.
The driving force comes from
o u t s i d e
and breaks the rules.
Your rude “of course”:
a sign you guess
a simple resolution.
That outside helpmeet,
will be used up,
fueling that crystal life.
That was the discovery.
No net drain,
but back and forth,
each feeding the other.
With this alone
(and only this)
the system breaks the dismal law
and lives forever.
(As a child, did you ever sing,
of giving away, and giving away,
and only having more?)
A physicist dreamed,
of a life like a crystal.
Collaboration made it real.
There’s something endlessly fascinating about the early days of quantum physics. In a century, we went from a few odd, inexplicable experiments to a practically complete understanding of the fundamental constituents of matter. Along the way the new ideas ended a world war, almost fueled another, and touched almost every field of inquiry. The people lucky enough to be part of this went from familiarly dorky grad students to architects of a new reality. Victor Weisskopf was one of those people, and The Joy of Insight: Passions of a Physicist is his autobiography.
Less well-known today than his contemporaries, Weisskopf made up for it with a front-row seat to basically everything that happened in particle physics. In the late 20’s and early 30’s he went from studying in Göttingen (including a crush on Maria Göppert before a car-owning Joe Mayer snatched her up) to a series of postdoctoral positions that would exhaust even a modern-day physicist, working in Leipzig, Berlin, Copenhagen, Cambridge, Zurich, and Copenhagen again, before fleeing Europe for a faculty position in Rochester, New York. During that time he worked for, studied under, collaborated or partied with basically everyone you might have heard of from that period. As a result, this section of the autobiography was my favorite, chock-full of stories, from the well-known (Pauli’s rudeness and mythical tendency to break experimental equipment) to the less-well known (a lab in Milan planned to prank Pauli with a door that would trigger a fake explosion when opened, which worked every time they tested it…and failed when Pauli showed up), to the more personal (including an in retrospect terrifying visit to the Soviet Union, where they asked him to critique a farming collective!) That era also saw his “almost Nobel”, in his case almost discovering the Lamb Shift.
Despite an “almost Nobel”, Weisskopf was paid pretty poorly when he arrived in Rochester. His story there puts something I’d learned before about another refugee physicist, Hertha Sponer, in a new light. Sponer’s university also didn’t treat her well, and it seemed reminiscent of modern academia. Weisskopf, though, thinks his treatment was tied to his refugee status: that, aware that they had nowhere else to go, universities gave the scientists who fled Europe worse deals than they would have in a Nazi-less world, snapping up talent for cheap. I could imagine this was true for Sponer as well.
Like almost everyone with the relevant expertise, Weisskopf was swept up in the Manhattan project at Los Alamos. There he rose in importance, both in the scientific effort (becoming deputy leader of the theoretical division) and the local community (spending some time on and chairing the project’s “town council”). Like the first sections, this surreal time leads to a wealth of anecdotes, all fascinating. In his descriptions of the life there I can see the beginnings of the kinds of “hiking retreats” physicists would build in later years, like the one at Aspen, that almost seem like attempts to recreate that kind of intense collaboration in an isolated natural place.
After the war, Weisskopf worked at MIT before a stint as director of CERN. He shepherded the facility’s early days, when they were building their first accelerators and deciding what kinds of experiments to pursue. I’d always thought that the “nuclear” in CERN’s name was an artifact of the times, when “nuclear” and “particle” physics were thought of as the same field, but according to Weisskopf the fields were separate and it was already a misnomer when the place was founded. Here the book’s supply of anecdotes becomes a bit more thin, and instead he spends pages on glowing descriptions of people he befriended. The pattern continues after the directorship as his duties get more administrative, spending time as head of the physics department at MIT and working on arms control, some of the latter while a member of the Pontifical Academy of Sciences (which apparently even a Jewish atheist can join). He does work on some science, though, collaborating on the “bag of quarks” model of protons and neutrons. He lives to see the fall of the Berlin wall, and the end of the book has a bit of 90’s optimism to it, the feeling that finally the conflicts of his life would be resolved. Finally, the last chapter abandons chronology altogether, and is mostly a list of his opinions of famous composers, capped off with a Bohr-inspired musing on the complementary nature of science and the arts, humanities, and religion.
One of the things I found most interesting in this book was actually something that went unsaid. Weisskopf’s most famous student was Murray Gell-Mann, a key player in the development of the theory of quarks (including coining the name). Gell-Mann was famously cultured (in contrast to the boorish-almost-as-affectation Feynman) with wide interests in the humanities, and he seems like exactly the sort of person Weisskopf would have gotten along with. Surprisingly though, he gets no anecdotes in this book, and no glowing descriptions: just a few paragraphs, mostly emphasizing how smart he was. I have to wonder if there was some coldness between them. Maybe Weisskopf had difficulty with a student who became so famous in his own right, or maybe they just never connected. Maybe Weisskopf was just trying to be generous: the other anecdotes in that part of the book are of much less famous people, and maybe Weisskopf wanted to prioritize promoting them, feeling that they were underappreciated.
Weisskopf keeps the physics light to try to reach a broad audience. This means he opts for short explanations, and often these are whatever is easiest to reach for. It creates some interesting contradictions: the way he describes his “almost Nobel” work in quantum electrodynamics is very much the way someone would have described it at the time, but very much not how it would be understood later, and by the time he talks about the bag of quarks model his more modern descriptions don’t cleanly link with what he said earlier. Overall, his goal isn’t really to explain the physics, but to explain the physicists. I enjoyed the book for that: people do it far too rarely, and the result was a really fun read.
Ask a doctor or a psychologist if they’re sure about something, and they might say “it has p<0.05”. Ask a physicist, and they’ll say it’s a “5 sigma result”. On the surface, they sound like they’re talking about completely different things. As it turns out, they’re not quite that different.
Whether it’s a p-value or a sigma, what scientists are giving you is shorthand for a probability. The p-value is the probability itself, while sigma tells you how many standard deviations something is away from the mean on a normal distribution. For people not used to statistics this might sound very complicated, but it’s not so tricky in the end. There’s a graph, called a normal distribution, and you can look at how much of it is above a certain point, measured in units called standard deviations, or “sigmas”. That gives you your probability.
What are these numbers a probability of? At first, you might think they’re a probability of the scientist being right: of the medicine working, or the Higgs boson being there.
That would be reasonable, but it’s not how it works. Scientists can’t measure the chance they’re right. All they can do is compare models. When a scientist reports a p-value, what they’re doing is comparing to a kind of default model, called a “null hypothesis”. There are different null hypotheses for different experiments, depending on what the scientists want to test. For the Higgs, scientists looked at pairs of photons detected by the LHC. The null hypothesis was that these photons were created by other parts of the Standard Model, like the strong force, and not by a Higgs boson. For medicine, the null hypothesis might be that people get better on their own after a certain amount of time. That’s hard to estimate, which is why medical experiments use a control group: a similar group without the medicine, to see how much they get better on their own.
Once we have a null hypothesis, we can use it to estimate how likely it is that it produced the result of the experiment. If there was no Higgs, and all those photons just came from other particles, what’s the chance there would still be a giant pile of them at one specific energy? If the medicine didn’t do anything, what’s the chance the control group did that much worse than the treatment group?
Ideally, you want a small probability here. In medicine and psychology, you’re looking for a 5% probability, for p<0.05. In physics, you need 5 sigma to make a discovery, which corresponds to a one in 3.5 million probability. If the probability is low, then you can say that it would be quite unlikely for your result to happen if the null hypothesis was true. If you’ve got a better hypothesis (the Higgs exists, the medicine works), then you should pick that instead.
Before this year’s prize was announced, I remember a few “water cooler chats” about who might win. No guess came close, though. The Nobel committee seems to have settled into a strategy of prizes on a loosely linked “basket” of topics, with half the prize going to a prominent theorist and the other half going to two experimental, observational, or (in this case) computational physicists. It’s still unclear why they’re doing this, but regardless it makes it hard to predict what they’ll do next!
When I read the announcement, my first reaction was, “surely it’s not that Parisi?” Giorgio Parisi is known in my field for the Altarelli-Parisi equations (more properly known as the DGLAP equations, the longer acronym because, as is often the case in physics, the Soviets got there first). These equations are in some sense why the scattering amplitudes I study are ever useful at all. I calculate collisions of individual fundamental particles, like quarks and gluons, but a real particle collider like the LHC collides protons. Protons are messy, interacting combinations of quarks and gluons. When they collide you need not merely the equations describing colliding quarks and gluons, but those that describe their messy dynamics inside the proton, and in particular how those dynamics look different for experiments with different energies. The equation that describes that is the DGLAP equation.
As it turns out, Parisi is known for a lot more than the DGLAP equation. He is best known for his work on “spin glasses”, models of materials where quantum spins try to line up with each other, never quite settling down. He also worked on a variety of other complex systems, including flocks of birds!
I don’t know as much about Manabe and Hasselmann’s work. I’ve only seen a few talks on the details of climate modeling. I’ve seen plenty of talks on other types of computer modeling, though, from people who model stars, galaxies, or black holes. And from those, I can appreciate what Manabe and Hasselmann did. Based on those talks, I recognize the importance of those first one-dimensional models, a single column of air, especially back in the 60’s when computer power was limited. Even more, I recognize how impressive it is for someone to stay on the forefront of that kind of field, upgrading models for forty years to stay relevant into the 2000’s, as Manabe did. Those talks also taught me about the challenge of coupling different scales: how small effects in churning fluids can add up and affect the simulation, and how hard it is to model different scales at once. To use these effects to discover which models are reliable, as Hasselmann did, is a major accomplishment.
I cleaned up my “Who Am I?” page this week, and some of you might notice my title changed. I’m no longer a Postdoc. As of this month, I’m an Assistant Professor.
Before you start congratulating me too much, saying I’ve made it and so on…to be clear, I’m not that kind of Assistant Professor.
Universities in Europe and the US work a bit differently. The US has the tenure-track system: professors start out tenure-track, and have a fixed amount of time to prove themselves. If they do, they get tenure, and essentially permanent employment. If not, they leave.
Some European countries are starting to introduce a tenure track, sometimes just university by university or job-by-job. For the rest, professors are divided not into tenured and tenure-track, but into permanent and fixed-term. Permanent professors are permanent in the way a normal employee of a company would be: they can still be fired, but if not their contract continues indefinitely. Fixed-term professors, then, have contracts for just a fixed span of time. In some cases this can be quite short. In my case, it’s one year.
Some US readers might be thinking this sounds a bit like an Adjunct. In a very literal sense that’s right, in Danish my title is Adjunkt. But it’s not the type of Adjunct you’re thinking of. US universities employ Adjuncts primarily for teaching. They’re often paid per class, and re-hired each year (though with no guarantees, leading to a lot of stress). That’s not my situation. I’m paid a fixed salary, and my primary responsibility is research, not teaching. I also won’t be re-hired next year, unless I find a totally different source of funding. Practically speaking, my situation is a lot like an extra year of Postdoc.
There are some differences. I’m paid a little more than I was as a Postdoc, and I have a few more perks. I’m getting more pedagogy training in the spring, I don’t know if I would have gotten that opportunity if I was still just a Postdoc. It’s an extra level of responsibility, and that does mean something.
But it does also mean I’m still looking for a job. Once again I find myself in application season: polishing my talks and crossing my fingers, not knowing exactly where I’ll end up.
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.
I’ve been digging through the WordPress “stats” page for this blog. One thing WordPress tells me is what links people follow to get here. It tells me how many times people come from Google or Facebook or Twitter, and how many come from seeing a link on another blog. One thing that surprised me is that some of the blogs people come here from haven’t updated in years.
The way I see it there are two possible explanations. It could be that new people keep checking the old blogs, see a link on their blogroll, and come on over here to check it out. But it could also be the same people over and over, who find it more convenient to start on an old blog and click on links from there.
WordPress doesn’t tell me the difference. But I realized, I can just ask. So in this post, I’m asking all my readers to tell me how you get here. I’m not asking how you found this blog to begin with, but rather how, on a typical day, you navigate to the site. Do you subscribe by email? Do you google the blog’s name every time? RSS reader? Let me know below! And if you don’t see an option that fits you, let me know in the comments!
It’s Valentine’s Day this weekend, so time for another physics poem. If you’d like to read the poems from past years, they’re archived with the tag Valentine’s Day Physics Poem, accessible here.
Passion is passion.
If you find yourself writing letter after letter,
be they “love”,
or “Physical Review”
Or if you are the quiet sort
and notice only in your mind
those questions, time after time
whenever silence reigns:
“how do I make things right?”
If you look ahead
and your branching,
each so different
still have one
If you could share that desert island, that jail cell,
and count yourself free.
You’ve found your star. Now it’s straight on till morning.
Last month, our local nest of science historians at the Niels Bohr Archive hosted a Zoom talk by Jed Z. Buchwald, a Newton scholar at Caltech. Buchwald had a story to tell about experimental uncertainty, one where Newton had an important role.
If you’ve ever had a lab course in school, you know experiments never quite go like they’re supposed to. Set a room of twenty students to find Newton’s constant, and you’ll get forty different answers. Whether you’re reading a ruler or clicking a stopwatch, you can never measure anything with perfect accuracy. Each time you measure, you introduce a little random error.
Textbooks worth of statistical know-how has cropped up over the centuries to compensate for this error and get closer to the truth. The simplest trick though, is just to average over multiple experiments. It’s so obvious a choice, taking a thousand little errors and smoothing them out, that you might think people have been averaging in this way through history.
They haven’t though. As far as Buchwald had found, the first person to average experiments in this way was Isaac Newton.
What did people do before Newton?
Well, what might you do, if you didn’t have a concept of random error? You can still see that each time you measure you get a different result. But you would blame yourself: if you were more careful with the ruler, quicker with the stopwatch, you’d get it right. So you practice, you do the experiment many times, just as you would if you were averaging. But instead of averaging, you just take one result, the one you feel you did carefully enough to count.
Before Newton, this was almost always what scientists did. If you were an astronomer mapping the stars, the positions you published would be the last of a long line of measurements, not an average of the rest. Some other tricks existed. Tycho Brahe for example folded numbers together pair by pair, averaging the first two and then averaging that average with the next one, getting a final result weighted to the later measurements. But, according to Buchwald, Newton was the first to just add everything together.
Even Newton didn’t yet know why this worked. It would take later research, theorems of statistics, to establish the full justification. It seems Newton and his later contemporaries had a vague physics analogy in mind, finding a sort of “center of mass” of different experiments. This doesn’t make much sense – but it worked, well enough for physics as we know it to begin.
So this Newtonmas, let’s thank the scientists of the past. Working piece by piece, concept by concept, they gave use the tools to navigate our uncertain times.