Atoms. Tokamaks. The latest Nobel Prize in in Physics. What do all of these have in common?

The answer: bagels. 

No, the answer to life, the universe, and everything isn’t 42 bagels, though Hitchhiker’s Guide to the Galaxy fans might argue otherwise. What matters here is a bagel’s shape: a bagel has one hole, and is thus in the shape of a torus.


The many shapes of atomic orbitals. Shown from top to bottom are s, p, d, and f orbitals.

The Atom

We’ll start by delving into the tiny world of the atom. Take a second to imagine how fast-moving objects form blurry patches of color. Similarly, in the atom, electrons move so quickly that they form a blur, known as an electron cloud. This cloud, or orbital, comes in many shapes: a sphere, a dumbbell, a bagel (torus), and more. Atoms create these clouds in specified orders and quantities: one spherical s orbital, three dumbbell-shaped p orbitals, and then five more exotically-shaped d orbitals. Four of the d orbitals are shaped like a pair of dumbbells crossed in the middle, while one looks like a dumbbell inserted through the hole of a bagel. In the d orbitals, electrons form a bagel shape common throughout our universe, on a tiny scale.

The Tokamak

Bagels not only exist throughout space, but are also used to study and discover things about it. The tokamak is a fusion reactor that uses magnetic fields to suspend plasma in the shape of a bagel. The circular “ring” of the bagel allows particles to flow in an uninterrupted circular loop, allowing the atoms to continue turning and accelerating in circles until they reach a high enough speed to collide and undergo nuclear fusion. As an added bonus, the shape also keeps the plasma from touching the sides of the machine.


Visualization of the plasma containment apparatus used in experimental fusion reactors. Coils (purple) are shown surrounding the plasma (rainbow).

The Nobel Prize

Imagine that you are baking bread, and that you have a ball of dough. You roll the ball of dough around and end up with a roll, or a structure with zero holes. The moment you poke a hole in that dough, though, you no longer have a roll — you now have a bagel, or a structure with one hole. There is no middle stage between roll and bagel, as the dough either has a hole, or it doesn’t; there is no such thing as half a hole (topologically speaking). You could then poke another hole into the dough and have two holes, but not one hole and a fraction of a hole.

In the same way, phase transitions either occur or don’t. There is no in between. However, for a long time researchers were doubtful about the ability of extremely thin or flat two-dimensional systems to change phase. Examples of such systems include very thin, zero-resistance superconductor sheets, or more exotically, very thin films of zero viscosity superfluid helium. Two of this year’s Nobel Prize winners, though, proved that transitions from one phase of matter to another can happen in these extremely thin surfaces. When the conductors are extremely cold, swirling vortices, or tiny loops of current, are found in pairs within the material. As the material warms up, these pairs break apart and the vortices move on their own. Again, the vortices are either paired or they aren’t, showing a mechanism for clean phase transitions to occur in cold, thin, materials, in the same way that bagels and dough can only transition from having one integer number of holes to another integer number of holes.

The next time you sit down for a bagel, remember that its shape can not only be found on the tiniest of scales, but can also function in the design of research equipment and provide clues into how exotic matter changes phase of matter. It’s a truly universal breakfast food.


About The Author

Ariel Chen