Congratulations to Thouless, Haldane, and Kosterlitz!

I’m traveling this week in sunny California, so I don’t have time for a long post, but I thought I should mention that the 2016 Nobel Prize in Physics has been announced. Instead of going to LIGO, as many had expected, it went to David Thouless, Duncan Haldane, and Michael Kosterlitz. LIGO will have to wait for next year.

Thouless, Haldane, and Kosterlitz are condensed matter theorists. While particle physics studies the world at the smallest scales and astrophysics at the largest, condensed matter physics lives in between, explaining the properties of materials on an everyday scale. This can involve inventing new materials, or unusual states of matter, with superconductors being probably the most well-known to the public. Condensed matter gets a lot less press than particle physics, but it’s a much bigger field: overall, the majority of physicists study something under the condensed matter umbrella.

This year’s Nobel isn’t for a single discovery. Rather, it’s for methods developed over the years that introduced topology into condensed matter physics.

Topology often gets described in terms of coffee cups and donuts. In topology, two shapes are the same if you can smoothly change one into another, so a coffee cup and a donut are really the same shape.

mug_and_torus_morphMost explanations stop there, which makes it hard to see how topology could be useful for physics. The missing part is that topology studies not just which shapes can smoothly change into each other, but which things, in general, can change smoothly into each other.

That’s important, because in physics most changes are smooth. If two things can’t change smoothly into each other, something special needs to happen to bridge the gap between them.

There are a lot of different sorts of implications this can have. Topology means that some materials can be described by a number that’s conserved no matter what (smooth) changes occur, leading to experiments that see specific “levels” rather than a continuous range of outcomes. It means that certain physical setups can’t change smoothly into other ones, which protects those setups from changing: an idea people are investigating in the quest to build a quantum computer, where extremely delicate quantum states can be disrupted by even the slightest change.

Overall, topology has been enormously important in physics, and Thouless, Haldane, and Kosterlitz deserve a significant chunk of the credit for bringing it into the spotlight.

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