Category Archives: Misc

Chaos: Warhammer 40k or Physics?

As I mentioned last week, it’s only natural to confuse chaos theory in physics with the forces of chaos in the game Warhammer 40,000. Since it will be Halloween in a few days, it’s a perfect time to explain the subtle differences between the two.

Warhammer 40kphysics
In the grim darkness of the far future, there is only war!In the grim darkness of Chapter 11 of Goldstein, Poole, and Safko, there is only Chaos!
Birthed from the psychic power of mortal mindsBirthed from the numerical computations of mortal physicists
Ruled by four chaos gods: Khorne, Tzeench, Nurgle, and SlaaneshRuled by three principles: sensitivity to initial conditions, topological transitivity, and dense periodic orbits
In the 31st millennium, nine legions of space marines leave humanity due to the forces of chaosIn the 3.5 millionth millennium, Mercury leaves the solar system due to the force of gravity
While events may appear unpredictable, everything is determined by Tzeench’s plansWhile events may appear unpredictable, everything is determined by the initial conditions
Humans drawn to strangely attractive cultsSystems in phase space drawn to strange attractors
Over time, cultists mutate, governed by the warpOver time, trajectories diverge, governed by the Lyapunov exponent
To resist chaos, the Imperium of Man demands strict spiritual controlTo resist chaos, the KAM Theorem demands strict mathematical conditions
Inspires nerds to paint detailed miniaturesInspires nerds to stick pendulums together
Fantasy version with confusing relation to the originalQuantum version with confusing relation to the original
Lots of cool gothic artPretty fractals

Congratulations to Alain Aspect, John F. Clauser and Anton Zeilinger!

The 2022 Nobel Prize was announced this week, awarded to Alain Aspect, John F. Clauser, and Anton Zeilinger for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science.

I’ve complained in the past about the Nobel prize awarding to “baskets” of loosely related topics. This year, though, the three Nobelists have a clear link: they were pioneers in investigating and using quantum entanglement.

You can think of a quantum particle like a coin frozen in mid-air. Once measured, the coin falls, and you read it as heads or tails, but before then the coin is neither, with equal chance to be one or the other. In this metaphor, quantum entanglement slices the coin in half. Slice a coin in half on a table, and its halves will either both show heads, or both tails. Slice our “frozen coin” in mid-air, and it keeps this property: the halves, both still “frozen”, can later be measured as both heads, or both tails. Even if you separate them, the outcomes never become independent: you will never find one half-coin to land on tails, and the other on heads.

For those who read my old posts, I think this is a much better metaphor than the different coin-cut-in-half metaphor I used five years ago.

Einstein thought that this couldn’t be the whole story. He was bothered by the way that measuring a “frozen” coin seems to change its behavior faster than light, screwing up his theory of special relativity. Entanglement, with its ability to separate halves of a coin as far as you liked, just made the problem worse. He thought that there must be a deeper theory, one with “hidden variables” that determined whether the halves would be heads or tails before they were separated.

In 1964, a theoretical physicist named J.S. Bell found that Einstein’s idea had testable consequences. He wrote down a set of statistical equations, called Bell inequalities, that have to hold if there are hidden variables of the type Einstein imagined, then showed that quantum mechanics could violate those inequalities.

Bell’s inequalities were just theory, though, until this year’s Nobelists arrived to test them. Clauser was first: in the 70’s, he proposed a variant of Bell’s inequalities, then tested them by measuring members of a pair of entangled photons in two different places. He found complete agreement with quantum mechanics.

Still, there was a loophole left for Einstein’s idea. If the settings on the two measurement devices could influence the pair of photons when they were first entangled, that would allow hidden variables to influence the outcome in a way that avoided Bell and Clauser’s calculations. It was Aspect, in the 80’s, who closed this loophole: by doing experiments fast enough to change the measurement settings after the photons were entangled, he could show that the settings could not possibly influence the forming of the entangled pair.

Aspect’s experiments, in many minds, were the end of the story. They were the ones emphasized in the textbooks when I studied quantum mechanics in school.

The remaining loopholes are trickier. Some hope for a way to correlate the behavior of particles and measurement devices that doesn’t run afoul of Aspect’s experiment. This idea, called, superdeterminism, has recently had a few passionate advocates, but speaking personally I’m still confused as to how it’s supposed to work. Others want to jettison special relativity altogether. This would not only involve measurements influencing each other faster than light, but also would break a kind of symmetry present in the experiments, because it would declare one measurement or the other to have happened “first”, something special relativity forbids. The majority, uncomfortable with either approach, thinks that quantum mechanics is complete, with no deterministic theory that can replace it. They differ only on how to describe, or interpret, the theory, a debate more the domain of careful philosophy than of physics.

After all of these philosophical debates over the nature of reality, you may ask what quantum entanglement can do for you?

Suppose you want to make a computer out of quantum particles, one that uses the power of quantum mechanics to do things no ordinary computer can. A normal computer needs to copy data from place to place, from hard disk to RAM to your processor. Quantum particles, however, can’t be copied: a theorem says that you cannot make an identical, independent copy of a quantum particle. Moving quantum data then required a new method, pioneered by Anton Zeilinger in the late 90’s using quantum entanglement. The method destroys the original particle to make a new one elsewhere, which led to it being called quantum teleportation after the Star Trek devices that do the same with human beings. Quantum teleportation can’t move information faster than light (there’s a reason the inventor of Le Guin’s ansible despairs of the materialism of “Terran physics”), but it is still a crucial technology for quantum computers, one that will be more and more relevant as time goes on.

Things Which Are Fluids

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.

More waters, please!

Some things in math look like berries, but are really like fluids. Take a polynomial, say 5 x^2 + 6 x + 8. It looks like three types of things, like three berries: five x^2, six x, and eight 1. Add another polynomial, and the illusion continues: add x^2 + 3 x + 2 and you get 6 x^2+9 x+10. You’ve just added more x^2, more x, more 1, 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 5(x^2+2x+1) - 4 (x+1) + 7. That’s the same thing, you can check. But now it looks like five x^2+2x+1, negative four x+1, and seven 1. 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.

Valentine’s Day Physics Poem 2022

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.

Time Crystals

A physicist once dreamed
of a life like a crystal.
Each facet the same, again and again,
     effortlessly
         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,
      not effortlessly,
	   but driven,
with reliable effort
input energy
(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,
doing work,
will be used up,
drained,
fueling that crystal life.

But no.

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,
alone, impossibly,
of a life like a crystal.

Collaboration made it real.

Book Review: The Joy of Insight

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.

Of p and sigma

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.

Give it a try: how much of this graph is past the 1\sigma line? How about 2\sigma?

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.

Note that this probability still uses a model: it’s the probability of the result given that the model is true. It isn’t the probability that the model is true, given the result. That probability is more important to know, but trickier to calculate. To get from one to the other, you need to include more assumptions: about how likely your model was to begin with, given everything else you know about the world. Depending on those assumptions, even the tiniest p-value might not show that your null hypothesis is wrong.

In practice, unfortunately, we usually can’t estimate all of those assumptions in detail. The best we can do is guess their effect, in a very broad way. That usually just means accepting a threshold for p-values, declaring some a discovery and others not. That limitation is part of why medicine and psychology demand p-values of 0.05, while physicists demand 5 sigma results. Medicine and psychology have some assumptions they can rely on: that people function like people, that biology and physics keep working. Physicists don’t have those assumptions, so we have to be extra-strict.

Ultimately, though, we’re all asking the same kind of question. And now you know how to understand it when we do.

Congratulations to Syukuro Manabe, Klaus Hasselmann, and Giorgio Parisi!

The 2021 Nobel Prize in Physics was announced this week, awarded to Syukuro Manabe and Klaus Hasselmann for climate modeling and Giorgio Parisi for understanding a variety of complex physical systems.

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 in to 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.

Four Gravitons and a…What Exactly Are You Now?

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 Few Advertisements

A couple different things that some of you might like to know about:

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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.

Poll: How Do You Get Here?

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!