If you're a topologist having breakfast, you're going to have a hard time telling the difference between your doughnut and your coffee mug. And that coffee in the mug might just as well be coffee ice or coffee steam.
Understand those two ideas and you've pretty much got this year's Nobel Prize in physics nailed. If not, maybe we should go a little further.
The prize, announced this morning, was awarded to American physicists David Thouless of the University of Washington, F. Duncan Haldane of Princeton University and J. Michael Kosterlitz of Brown University, who are being honored for work they did in the 1970s and 1980s involving what is broadly being called "exotic matter." Forty years is awful long time to wait for recognition, but in the field of physics it makes sense since the concepts can be so abstruse it sometimes takes that long just to make sure they shake out and hold up.
Start with the coffee mug and the doughnut. Topologists study shapes in three-dimensional (or sometimes even two- or one-dimensional) space, but do so in a theoretical world in which all matter is clay-like and mutable. A baseball could thus be stretched into a baseball bat, then flattened down to home plate, with no loss of topological integrity. What the baseball could never become however, is a catcher's mitt, because a catcher's mitt has holes and gaps in it, and topology does not allow you to create those de novo. That's why the coffee mug, which has the single hole formed by its handle, could become a doughnut, but it can never become a pretzel, which has three holes.
It's mind-game nonsense—except it's not. Topology has real-world applications in mathematics, robotics, computer programming and even biology, with scientists wanting to learn more about the different ways DNA folds, twists and knots.
The business with the coffee, steam and ice involves the far more basic idea of phase changes. There are a handful of types of chemical phase changes beyond freezing and boiling—as when a glowing plasma loses its electrical energy and eases back down to become an ordinary gas again (recombination), or when a gas settles onto a surface to form a solid layer (deposition). Much basic chemistry is driven by phase changes, and similar patterns play out in the real world. Traffic moving more and more slowly until it freezes into pure gridlock can be looked at as a form of phase change; so too can an orderly house of cards—or even an actual house—that grows increasingly unstable until it collapses into an entropic pile. The more we know about all of these transitions the better we can control and manipulate them.
What the three new Laureates did that made them so prize-worthy was, among other things, extend topology and phase changes to the fields of superconductivity and superfluidity. Superconductivity, as its name suggests, occurs when a material becomes so highly conductive that electricity moves through it with zero resistance. Superfluidity is a similar state that is achieved when liquids flow with no viscosity at all, meaning no loss of kinetic energy as they move. (Picture ketchup becoming as runny as water, and water then becoming runnier still until it is effectively moving without friction.)
Thouless, Haldane and Kosterlitz found that at different energy levels or at supercold temperatures, topological phase transitions can occur in thin films of matter, causing tight pairs of vortices that spin in close proximity to separate—a little like a catamaran separating into two free-floating boats—and that has superconductive and superfluid implications. That doesn't quite upend existing topology—as it would if a second or third hole appeared out of nowhere. But in terms of the behavior of the material it's close, as illustrations (above) released by the Nobel Committee reveal. The prize-winners also showed that these changes happen in predictable integers or steps, like the thermometer falling a degree at a time until it reaches 32º F or 0º C and water freezes.
Nobody in Stockholm, where the Nobel Committee meets, pretends that any of this has immediate applications, but it will. Superconductivity and superfluidity occurring in extremely thin layers have very real potential in all matter of engineering fields, including computing. And better understanding of phase transitions and states of exotic matter can be helpful in simulating and studying quantum states. It's not as straightforward as doughnuts and coffee, but eventually it will be vastly more important.