Thursday, May 31, 2018

Dig in to the Physics of Donuts for National Donut Day!

Before you ingest your annual delicious (possibly free) treat for Friday's annual celebration, why not learn about the physics of donuts? From topology to nuclear fusion, donuts are the physicist's breakfast pastry of choice. Not just because they’re tasty, but because their shape, the torus, is the subject of fascinating physics. Let's dig in to some of the multitude of donut sightings in physics, and answer the age-old question: Which rolls downhill faster, the holed donut or the filled doughnut?
A selection of Dunkin's finest research materials.
Physicists love donuts. Croissants? Not so much: physicists discuss “donuts” or “doughnuts” 544 times in papers published in the Physical Review journals. Croissants are mentioned only eleven times.

The most recent Physical Review paper that mentions donuts explains how to make flying electromagnetic donuts in a lab! The paper was published last week, and explains how to use novel metamaterials to build a machine to launch doughnut-like structures made of electric and magnetic fields. It might sound flippant, but these "donuts"essentially constitute a never-before-seen kind of photon, which could have useful applications in all sorts of fields.

Flying Electromagnetic Donuts.
Courtesy of Physical Review B.

This being a physics blog, we're contractually obligated to take this opportunity to bring up the only decent topology one-liner that's ever been told: topologists can't tell their donuts from their coffee cups! From the point of view of people who think about topology, anything that has a certain number of holes in it can be morphed into any other shape with the same number of holes. Doughnuts have one hole, and so do coffee cups (the hole in the handle), so topologically they’re the same. The Nobel Prize committee used this very idea when they announced the 2016 Physics Nobel Prize.

Eyeglasses are more electrically conductive than donuts and coffee mugs, but less so than pretzels. Obviously.
Image Credit:  Johan Jarnestad/The Royal Swedish Academy of Sciences

Not all donut physics is so exciting, though. For instance, donut-shaped soap bubbles would be really cool, but according to a paper published in Physical Review E in 2015, they aren’t stable and break apart into spheres almost instantly. So don’t even think about it–it’ll just make you sad that we can’t have nice things.

Sadly not a donut-shaped bubble.
How about some donut fusion? No, we're not talking the Cronut (which just passed its fifth birthday). In the quest for stable thermonuclear fusion, the donut has reigned supreme since the mid-1970s. Magnetic confinement of plasma is most efficient with a donut shape, a type of reactor called a tokamak.

Inner view of a tokamak, a donut-shaped fusion reactor.
Image credit: CRPP-EPFL, Association Suisse-Euratom
String theory's extra dimensions are in a donut! We live in a world with three dimensions, but in string theory, there may be ten, eleven, or twenty-six. But, you might ask, if string theory is correct, why don’t we see way more than the 3D world? One possible answer is that the extra dimensions are curled in really, really, really, really, really tiny donuts. OK, string theorists don’t use the word donut; they prefer "torus". Whatever. Same (multi-dimensional) shape. How delicious must a six dimensional donut be, I wonder?

Now for the important questions.

Toroidal donuts can roll, but so can the cylindrical cream-filled donuts. Which donut will roll faster?

Our hypothesis predicted the filled donut would roll faster than a regular donut. This follows the classic physics experiment comparing the moment of inertia of a disc vs. a hoop.  However, experiments don't always go according to plan.

In our test, the filled one was slower—but that seems to violate classical physics. The problem could be that donuts aren't as round as we would like for the test, behaving kind of like a flat tire, so our intrepid intern, Amanda, made idealized donuts out of cardboard.

Idealized donuts.
Not safe for human consumption.
The solid disc represents a cream filled donut. The one with a small hole is Amanda’s best approximation of one of Dunkin’s classics.

This went a little more like Galileo would have expected. The filled donut was fastest, as we would have expected, the one with the smaller hole was nearly as fast, and the hoop-like donut brought up the rear:

Before we go: a word about words. You can buy donut holes at a store, but they aren’t the little balls made of dough. Those little balls are anti-donut holes. A donut hole is the center of a donut, where there is no dough...or it's the hole in your head when you open your mouth. How do I know this? When a particle meets an antiparticle, they annihilate—the particle and the antiparticle both disappear. Here’s a clip of our buddy James demonstrating particle-antiparticle annihilation as he introduces an anti-donut hole to his donut hole. You’re welcome.

Anti-donut hole to donut hole annihilation.
Perhaps an even more accurate analogy would be the one between electrons and "electron holes"—places in an atomic lattice where you'd ordinarily find an electron, but it's been knocked out by extra energy. These electron holes, little pockets of nothing in a sea of negative charge, behave like little positive charges—and when an electron falls back into one, it can give off energy as a photon!

Happy National Doughnut Day, from your friends at Physics Buzz.

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