# Things I’d Like to Know More About

This is an accountability post, of sorts.

As a kid, I wanted to know everything. Eventually, I realized this was a little unrealistic. Doomed to know some things and not others, I picked physics as a kind of triage. Other fields I could learn as an outsider: not well enough to compete with the experts, but enough to at least appreciate what they were doing. After watching a few string theory documentaries, I realized this wasn’t the case for physics: if I was going to ever understand what those string theorists were up to, I would have to go to grad school in string theory.

Over time, this goal lost focus. I’ve become a very specialized creature, an “amplitudeologist”. I didn’t have time or energy for my old questions. In an irony that will surprise no-one, a career as a physicist doesn’t leave much time for curiosity about physics.

One of the great things about this blog is how you guys remind me of those old questions, bringing me out of my overspecialized comfort zone. In that spirit, in this post I’m going to list a few things in physics that I really want to understand better. The idea is to make a public commitment: within a year, I want to understand one of these topics at least well enough to write a decent blog post on it.

Wilsonian Quantum Field Theory:

When you first learn quantum field theory as a physicist, you learn how unsightly infinite results get covered up via an ad-hoc-looking process called renormalization. Eventually you learn a more modern perspective, that these infinite results show up because we’re ignorant of the complete theory at high energies. You learn that you can think of theories at a particular scale, and characterize them by what happens when you “zoom” in and out, in an approach codified by the physicist Kenneth Wilson.

While I understand the basics of Wilson’s approach, the courses I took in grad school skipped the deeper implications. This includes the idea of theories that are defined at all energies, “flowing” from an otherwise scale-invariant theory perturbed with extra pieces. Other physicists are much more comfortable thinking in these terms, and the topic is important for quite a few deep questions, including what it means to properly define a theory and where laws of nature “live”. If I’m going to have an informed opinion on any of those topics, I’ll need to go back and learn the Wilsonian approach properly.

Wormholes:

If you’re a fan of science fiction, you probably know that wormholes are the most realistic option for faster-than-light travel, something that is at least allowed by the equations of general relativity. “Most realistic” isn’t the same as “realistic”, though. Opening a wormhole and keeping it stable requires some kind of “exotic matter”, and that matter needs to violate a set of restrictions, called “energy conditions”, that normal matter obeys. Some of these energy conditions are just conjectures, some we even know how to violate, while others are proven to hold for certain types of theories. Some energy conditions don’t rule out wormholes, but instead restrict their usefulness: you can have non-traversable wormholes (basically, two inescapable black holes that happen to meet in the middle), or traversable wormholes where the distance through the wormhole is always longer than the distance outside.

I’ve seen a few talks on this topic, but I’m still confused about the big picture: which conditions have been proven, what assumptions were needed, and what do they all imply? I haven’t found a publicly-accessible account that covers everything. I owe it to myself as a kid, not to mention everyone who’s a kid now, to get a satisfactory answer.

Quantum Foundations:

Quantum Foundations is a field that many physicists think is a waste of time. It deals with the questions that troubled Einstein and Bohr, questions about what quantum mechanics really means, or why the rules of quantum mechanics are the way they are. These tend to be quite philosophical questions, where it’s hard to tell if people are making progress or just arguing in circles.

I’m more optimistic about philosophy than most physicists, at least when it’s pursued with enough analytic rigor. I’d like to at least understand the leading arguments for different interpretations, what the constraints on interpretations are and the main loopholes. That way, if I end up concluding the field is a waste of time at least I’d be making an informed decision.

You might notice a change on the site this week: the ads are gone!

When I started this blog back in 2012, it was just a class project. I didn’t want to spend money on it, so I chose WordPress.com’s free hosting option. A consequence of that option is that WordPress got to post ads. These were pretty mild to begin with, I think most of the early posts didn’t even have ads. It seemed like a reasonable deal.

Over the years, WordPress has quietly been adding more ads, and worse ones. I mostly hadn’t noticed: I use an adblocker. For those who don’t, though, the blog began to look increasingly unprofessional, plastered with the kind of shitty, borderline-scam ads that fill certain parts of the internet. Thanks to everyone who let me know this was happening, I don’t think I would have noticed otherwise. To clarify, I never made any money from these ads, all of the revenue went to WordPress.

As of this week I’ve switched the site to a paid hosting plan. The move is long overdue: the plan is actually pretty cheap, and is the sort of thing I could have easily afforded by myself. As it happens I don’t have to afford it by myself: the grant that funds me, a Marie Curie Individual Fellowship, also funds outreach activities. I already had a message thanking them on my About page, but somehow I hadn’t considered actually using their funding here.

The site’s new plan also comes with a free domain, so you can now reach this site with a new simpler address: 4gravitons.com. The old 4gravitons.wordpress.com address should still work as well, if there are any glitches please let me know!

# Pi Day Alternatives

On Pi Day, fans of the number pi gather to recite its digits and eat pies. It is the most famous of numerical holidays, but not the only one. Have you heard of the holidays for other famous numbers?

Tau Day: Celebrated on June 28. Observed by sitting around gloating about how much more rational one is than everyone else, then getting treated with high-energy tau leptons for terminal pedantry.

Canadian Modular Pi Day: Celebrated on February 3. Observed by confusing your American friends.

e Day: Celebrated on February 7. Observed in middle school classrooms, explaining the wonders of exponential functions and eating foods like eggs and eclairs. Once the students leave, drop tabs of ecstasy instead.

Golden Ratio Day: Celebrated on January 6. Rub crystals on pyramids and write vaguely threatening handwritten letters to every physicist you’ve heard of.

Euler Gamma Day: Celebrated on May 7 by dropping on the floor and twitching.

Riemann Zeta Daze: The first year, forget about it. The second, celebrate on January 6. The next year, January 2. After that, celebrate on New Year’s Day earlier and earlier in the morning each year until you can’t tell the difference any more.

# Valentine’s Day Physics Poem 2019

It’s that time of year again! Time for me to dig in to my files and bring you yet another of my old physics poems.

Plagued with Divergences

“The whole scheme of local field theory is plagued with divergences”

Is divergence ever really unexpected?

If you asked a computer, what would it tell you?

You’d hear a whirring first, lungs and heart of the machine beating faster and faster.

And you’d dismiss it.
You knew this wasn’t going to be an easy interaction.
It doesn’t mean you’re going to diverge.

And perhaps it would try to warn you, write it there on the page.
It might even notice, its built-in instincts telling you, by the book,
“This will diverge.”

But instincts lie, and builders cheat.
And it doesn’t mean you’re going to diverge.

Now, you do everything the slow way,
Numerically.
Dismiss your instincts and force yourself through
Piece by piece.

And now, you can’t stop hearing the whir
The machine’s beating heart
Even when it should be at rest

And step by step, it tries to minimize its errors
And step by step, the errors grow

And exhausted, in the end, you see splashed across the screen
Something bigger than it should ever have been.

But sometimes things feel big and strange.
That’s just the way of the big wide world.
And it doesn’t mean you’re going to diverge.

You could have seen the signs,
Power-counted, seen what could overwhelm.
And you could have regulated, with an epsilon of flexibility.

But this one, this time, was supposed to be
Needed to be
Physical Truth
And truth doesn’t diverge

So you keep going,
Wheezing breath and painstaking calculation,
And every little thing blowing up

It’s not like there’s a better way to live.

# Book Review: Thirty Years That Shook Physics and Mr Tompkins in Paperback

George Gamow was one of the “quantum kids” who got their start at the Niels Bohr Institute in the 30’s. He’s probably best known for the Alpher, Bethe, Gamow paper, which managed to combine one of the best sources of evidence we have for the Big Bang with a gratuitous Greek alphabet pun. He was the group jester in a lot of ways: the historians here have archives full of his cartoons and in-jokes.

Naturally, he also did science popularization.

I recently read two of Gamow’s science popularization books, “Mr Tompkins” and “Thirty Years That Shook Physics”. Reading them was a trip back in time, to when people thought about physics in surprisingly different ways.

“Mr. Tompkins” started as a series of articles in Discovery, a popular science magazine. They were published as a book in 1940, with a sequel in 1945 and an update in 1965. Apparently they were quite popular among a certain generation: the edition I’m reading has a foreword by Roger Penrose.

(As an aside: Gamow mentions that the editor of Discovery was C. P. Snow…that C. P. Snow?)

Mr Tompkins himself is a bank clerk who decides on a whim to go to a lecture on relativity. Unable to keep up, he falls asleep, and dreams of a world in which the speed of light is much slower than it is in our world. Bicyclists visibly redshift, and travelers lead much longer lives than those who stay at home. As the book goes on he meets the same professor again and again (eventually marrying his daughter) and sits through frequent lectures on physics, inevitably falling asleep and experiencing it first-hand: jungles where Planck’s constant is so large that tigers appear as probability clouds, micro-universes that expand and collapse in minutes, and electron societies kept strictly monogamous by “Father Paulini”.

The structure definitely feels dated, and not just because these days people don’t often go to physics lectures for fun. Gamow actually includes the full text of the lectures that send Mr Tompkins to sleep, and while they’re not quite boring enough to send the reader to sleep they are written on a higher level than the rest of the text, with more technical terms assumed. In the later additions to the book the “lecture” aspect grows: the last two chapters involve a dream of Dirac explaining antiparticles to a dolphin in basically the same way he would explain them to a human, and a discussion of mesons in a Japanese restaurant where the only fantastical element is a trio of geishas acting out pion exchange.

Some aspects of the physics will also feel strange to a modern audience. Gamow presents quantum mechanics in a way that I don’t think I’ve seen in a modern text: while modern treatments start with uncertainty and think of quantization as a consequence, Gamow starts with the idea that there is a minimum unit of action, and derives uncertainty from that. Some of the rest is simply limited by timing: quarks weren’t fully understood even by the 1965 printing, in 1945 they weren’t even a gleam in a theorist’s eye. Thus Tompkins’ professor says that protons and neutrons are really two states of the same particle and goes on to claim that “in my opinion, it is quite safe to bet your last dollar that the elementary particles of modern physics [electrons, protons/neutrons, and neutrinos] will live up to their name.” Neutrinos also have an amusing status: they hadn’t been detected when the earlier chapters were written, and they come across rather like some people write about dark matter today, as a silly theorist hypothesis that is all-too-conveniently impossible to observe.

“Thirty Years That Shook Physics”, published in 1966, is a more usual sort of popular science book, describing the history of the quantum revolution. While mostly focused on the scientific concepts, Gamow does spend some time on anecdotes about the people involved. If you’ve read much about the time period, you’ll probably recognize many of the anecdotes (for example, the Pauli Principle that a theorist can break experimental equipment just by walking in to the room, or Dirac’s “discovery” of purling), even the ones specific to Gamow have by now been spread far and wide.

Like Mr Tompkins, the level in this book is not particularly uniform. Gamow will spend a paragraph carefully defining an average, and then drop the word “electroscope” as if everyone should know what it is. The historical perspective taught me a few things I perhaps should have already known, but found surprising anyway. (The plum-pudding model was an actual mathematical model, and people calculated its consequences! Muons were originally thought to be mesons!)

Both books are filled with Gamow’s whimsical illustrations, something he was very much known for. Apparently he liked to imitate other art styles as well, which is visible in the portraits of physicists at the front of each chapter.

1966 was late enough that this book doesn’t have the complacency of the earlier chapters in Mr Tompkins: Gamow knew that there were more particles than just electrons, nucleons, and neutrinos. It was still early enough, though, that the new particles were not fully understood. It’s interesting seeing how Gamow reacts to this: his expectation was that physics was on the cusp of another massive change, a new theory built on new fundamental principles. He speculates that there might be a minimum length scale (although oddly enough he didn’t expect it to be related to gravity).

It’s only natural that someone who lived through the dawn of quantum mechanics should expect a similar revolution to follow. Instead, the revolution of the late 60’s and early 70’s was in our understanding: not new laws of nature so much as new comprehension of just how much quantum field theory can actually do. I wonder if the generation who lived through that later revolution left it with the reverse expectation: that the next crisis should be solved in a similar way, that the world is quantum field theory (or close cousins, like string theory) all the way down and our goal should be to understand the capabilities of these theories as well as possible.

The final section of the book is well worth waiting for. In 1932, Gamow directed Bohr’s students in staging a play, the “Blegdamsvej Faust”. A parody of Faust, it features Bohr as god, Pauli as Mephistopheles, and Ehrenfest as the “erring Faust” (Gamow’s pun, not mine) that he tempts to sin with the promise of the neutrino, Gretchen. The piece, translated to English by Gamow’s wife Barbara, is filled with in-jokes on topics as obscure as Bohr’s habitual mistakes when speaking German. It’s gloriously weird and well worth a read. If you’ve ever seen someone do a revival performance, let me know!

# A Newtonmas Present of Internet Content

I’m lazy this Newtonmas, so instead of writing a post of my own I’m going to recommend a few other people who do excellent work.

Quantum Frontiers is a shared blog updated by researchers connected to Caltech’s Institute for Quantum Information and Matter. While the whole blog is good, I’m going to be more specific and recommend the posts by Nicole Yunger Halpern. Nicole is really a great writer, and her posts are full of vivid imagery and fun analogies. If she’s not as well-known, it’s only because she lacks the attention-grabbing habit of getting into stupid arguments with other bloggers. Definitely worth a follow.

Recommending Slate Star Codex feels a bit strange, because it seems like everyone I’ve met who would enjoy the blog already reads it. It’s not a physics blog by any stretch, so it’s also an unusual recommendation to give here. Slate Star Codex writes about a wide variety of topics, and while the author isn’t an expert in most of them he does a lot more research than you or I would. If you’re interested in up-to-date meta-analyses on psychology, social science, and policy, pored over by someone with scrupulous intellectual honesty and an inexplicably large amount of time to indulge it, then Slate Star Codex is the blog for you.

I mentioned Piled Higher and Deeper a few weeks back, when I reviewed the author’s popular science book We Have No Idea. Piled Higher and Deeper is a webcomic about life in grad school. Humor is all about exaggeration, and it’s true that Piled Higher and Deeper exaggerates just how miserable and dysfunctional grad school can be…but not by as much as you’d think. I recommend that anyone considering grad school read Piled Higher and Deeper, and take it seriously. Grad school can really be like that, and if you don’t think you can deal with spending five or six years in the world of that comic you should take that into account.

# Congratulations to Arthur Ashkin, Gérard Mourou, and Donna Strickland!

The 2018 Physics Nobel Prize was announced this week, awarded to Arthur Ashkin, Gérard Mourou, and Donna Strickland for their work in laser physics.

Some Nobel prizes recognize discoveries of the fundamental nature of reality. Others recognize the tools that make those discoveries possible.

Ashkin developed techniques that use lasers to hold small objects in place, culminating in “optical tweezers” that can pick up and move individual bacteria. Mourou and Strickland developed chirped pulse amplification, the current state of the art in extremely high-power lasers. Strickland is only the third woman to win the Nobel prize in physics, Ashkin at 96 is the oldest person to ever win the prize.

(As an aside, the phrase “optical tweezers” probably has you imagining two beams of laser light pinching a bacterium between them, like microscopic lightsabers. In fact, optical tweezers use a single beam, focused and bent so that if an object falls out of place it will gently roll back to the middle of the beam. Instead of tweezers, it’s really more like a tiny laser spoon.)

The Nobel announcement emphasizes practical applications, like eye surgery. It’s important to remember that these are research tools as well. I wouldn’t have recognized the names of Ashkin, Mourou, and Strickland, but I recognized atom trapping, optical tweezers, and ultrashort pulses. Hang around atomic physicists, or quantum computing experiments, and these words pop up again and again. These are essential tools that have given rise to whole subfields. LIGO won a Nobel based on the expectation that it would kick-start a vast new area of research. Ashkin, Mourou, and Strickland’s work already has.

# Elliptic Integrals in Ascona

I’m at a conference this week, Elliptic Integrals in Mathematics and Physics, in Ascona, Switzerland.

Perhaps the only place where the view rivals Les Houches

Elliptic integrals are the next frontier after polylogarithms, more complicated functions that can come out of Feynman diagrams starting at two loops. The community of physicists studying them is still quite small, and a large fraction of them are here at this conference. We’re at the historic Monte Verità conference center, and we’re not even a big enough group to use their full auditorium.

There has been an impressive amount of progress in understanding these integrals, even just in the last year. Watching the talks, it’s undeniable that our current understanding is powerful, broad…and incomplete. In many ways the mysteries of the field are clearing up beautifully, with many once confusingly disparate perspectives linked together. On the other hand, it feels like we’re still working with the wrong picture, and I suspect there’s still a major paradigm shift in the future. All in all, the perfect time to be working on elliptics!

# At Least One Math Term That Makes Sense

I’ve complained before about how mathematicians name things. Mathematicans seem to have a knack for taking an ordinary bland word that’s almost indistinguishable from the other ordinary, bland words they’ve used before and assigning it an incredibly specific mathematical concept. Varieties and forms, motives and schemes, in each case you end up wishing they picked a word that was just a little more descriptive.

Sometimes, though, a word may seem completely out of place when it actually has a fairly reasonable explanation. Such is the case for the word “period“.

Suppose you want to classify numbers. You have the integers, and the rational numbers. A bigger class of numbers are “algebraic”, in that you can get them “from algebra”: more specifically, as solutions of polynomial equations with rational coefficients. Numbers that aren’t algebraic are “transcendental”, a popular example being $\pi$.

Periods lie in between: a set that contains algebraic numbers, but also many of the transcendental numbers. They’re numbers you can get, not from algebra, but from calculus: they’re integrals over rational functions. These numbers were popularized by Kontsevich and Zagier, and they’ve led to a lot of fruitful inquiry in both math and physics.

But why the heck are they called periods?

Think about $e^{i x}$.

Or if you prefer, think about a circle

$e^{i x}$ is a periodic function, with period $2\pi$.  Take $x$ from $0$ to $2\pi$ and the function repeats, you’ve traveled in a circle.

Thought of another way, $2\pi$ is the volume of the circle. It’s the integral, around the circle, of $\frac{dz}{z}$. And that integral nicely matches Kontsevich and Zagier’s definition of a period.

The idea of a period, then, comes from generalizing this. What happens when you only go partway around the circle, to some point $z$ in the complex plane? Then you need to go to a point $x=-i \ln z$. So a logarithm can also be thought of as measuring the period of $e^{i x}$. And indeed, since a logarithm can be expressed as $\int\frac{dz}{z}$, they count as periods in the Kontsevich-Zagier sense.

Starting there, you can loosely think about the polylogarithm functions I like to work with as collections of logs, measuring periods of interlocking circles.

And if you need to go beyond polylogarithms, when you can’t just go circle by circle?

Then you need to think about functions with two periods, like Weierstrass’s elliptic function. Just as you can think about $e^{i x}$ as a circle, you can think of Weierstrass’s function in terms of a torus.

Obligatory donut joke here

The torus has two periods, corresponding to the two circles you can draw around it. The periods of Weierstrass’s function are transcendental numbers, and they fit Kontsevich and Zagier’s definition of periods. And if you take the inverse of Weierstrass’s function, you get an elliptic integral, just like taking the inverse of $e^{i x}$ gives a logarithm.

So mathematicians, I apologize. Periods, at least, make sense.

# Valentine’s Day Physics Poem 2018

Valentine’s Day was this week, so long-time readers should know what to expect. To continue this blog’s tradition, I’m posting another one of my old physics poems.

Winding Number One

When you feel twisted up inside, you may be told to step back

That after a long time, from a long distance

All things fall off.

So I stepped back.

But looking in from a distance

On the border (at infinity)

A shape remained

Etched deep

In the equation of my being

A shape that wouldn’t fall off

Even at infinity.

And they may tell you to wait and see,

That you will evolve in time

That all things change, continuously.

So I let myself change.

But no matter how long I waited

How much I evolved

I could not return

My new state cannot be deformed

To what I was before.

The shape at my border

Is basic, immutable.

Faced with my thoughts

I try to draw a map

And run out of space.

I need two selves

Two lives

To map my soul.

A double cover.

And now, faced by my dual

Tracing each index

Integrated over manifold possibilities

We do not vanish

We have winding number one.