A Nobel that helps explain the hole in a bagel

The announcement of the 2016 Nobel Prize in Physics seems to have left many people perplexed.

Three physicists -- Michael Kosterlitz, David Thouless and Duncan Haldane -- received the prize for work on "topological phase transitions and topological states of matter." Scientists at the awards press conference vaguely implied it had something to do with the holes in bagels and pretzels, and with topology, an arcane branch of mathematics.

And yet, the work isn't as obscure as it may seem. It's one more step in the study of ordinary matter that has been going on for centuries.

Substances often change form; make some water cold enough, and it will abruptly freeze. The water molecules don't change, only their organization does: the molecules that moved freely in the liquid at the higher temperature, when they had more energy, suddenly get locked in place, making a solid. Physicists call this a phase transition, and similar transformations of organization happen everywhere -- in crystals, magnetic materials, superconductors, you name it. Making anything from good steel alloys to tasty chocolate requires careful control over such organizational changes.

Scientists have known about phase transitions for centuries, of course, yet physicists really only gained a deep understanding of them in the 1960s and early '70s. One thing they discovered is quite amazing -- that such changes, even in totally different materials that would seem to have almost nothing in common, often happen in exactly the same way. For example, phase transitions in some liquids, metals and magnetic materials are exactly identical, despite there being almost no physical similarities in the substances. There are zillions of different physical materials, yet across the board, when organization changes from one form to another, it typically happens in one of a very small number of ways.

Most physical stuff exists in three dimensions, of course, but physicists can also make extremely thin two-dimensional films or even microscopically fine one-dimensional wires. What happens to phase transitions in these weirder conditions? Here, it turns out, the beautiful 1970s theory implied for various reasons that in many real systems, they should simply never occur. But in 1973, Kosterlitz and Thouless found a loophole in the theory.

Think of the surface of a liquid, which is a two-dimension system. One unique thing about it is that it can support vortices, or regions of circular flow. In fact, it can have vortices of two kinds, clockwise or counterclockwise, which we might call a vortex and an anti-vortex. In a liquid, it's easy to stir up a pair of vortices -- one vortex and one anti-vortex -- by running a finger through it. Kosterlitz and Thouless showed that for two-dimensional systems much more generally -- sadly, the analogy to the liquid surface only goes so far -- that the ordinary jostling of atoms associated with temperature should stir up vortex pairs like this all the time, creating a kind of gas of weakly bound vortex pairs. They also showed that, as temperature increases, these pairs should eventually get ripped apart, shifting the system's organization from one form to another -- a phase transition in two dimensions, and of a kind never before imagined by physicists.

What about the bagels and pretzels? Topology is the study of properties of objects that remain unchanged even as the object gets distorted and stretched. Stretch a rubber bagel into any weird shape you like -- without ripping it -- and you'll always only have a single hole. Vortices in two dimensions work much like holes, and with the mathematics of topology, Kosterlitz and Thouless were able to add another layer to our fundamental understanding of how, in our world, one kind of organization can give way to another. (Some visuals of the transition really help, and I recommend physicist John Baez's excellent explanation.)

And, sure enough, this thing turns out to happen in real physical systems. It's been seen in thin films of both superconducting solids and superfluid helium, as well as in the melting of fragile two dimensional solids. This matter is "exotic" in the sense that it doesn't exist in nature, even though physicists build it up out of the ordinary particles that make up everything else. The third Nobel winner, Duncan Haldane, did important work also using topological concepts, culminating in the recent discover of solids called topological insulators, weird materials that don't conduct electricity on the inside, but do at their surfaces, again for topological reasons.

When people think of physics, they usually think of Albert Einstein or quantum theory or Stephen Hawking and cosmology. But most physics during the past 50 years has been in so-called "condensed matter physics" -- the study of the stuff around us, the liquids, solids, gases and everything else from plastics to superconductors. It's all about understanding the kinds of organization that are possible, and how they can change form. This Nobel work fits within a very old tradition.

Buchanan, a physicist and science writer, is the author of the book "Forecast: What Physics, Meteorology and the Natural Sciences Can Teach Us About Economics."