
Scientific Background on the Nobel Prize in Physics 2016 [pdf] - mathgenius
https://www.nobelprize.org/nobel_prizes/physics/laureates/2016/advanced-physicsprize2016.pdf
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mathgenius
John Baez has a nice write-up aswell:
[https://johncarlosbaez.wordpress.com/2016/10/07/kosterlitz-t...](https://johncarlosbaez.wordpress.com/2016/10/07/kosterlitz-
thouless-transition/)

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ajkjk
This paper mentions that vortices in a 2d system of phases end up acting like
particles that obey a 1/r force law, which is _so cool_ to me. Instead of
thinking 'vortices act like particles' I prefer 'whoa, particles act like
vortices'. Electrons and positrons annihilate when they meet in much the same
way that a vortex plus an antivortex do (except they give off photons, so
maybe they're just 'more complicated' vortices in some way?).

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dnautics
there's some crank out there with a "vortex theory of the universe". But from
you description it seems like vortex is a subset of particles (but not the
other way) because there are plenty of particles that don't obey 1/r force
laws. Moreover, extending vortices to three dimensions is tricky, due to the
hairy ball theorem.

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ajkjk
The 1/r thing is just emergent from it being a 2d space, since the surface
area of a 2d ball goes as 'r', a divergenceless field goes as 1/r (since the
flux through any contour around the particle ought to be constant). In 3d this
would correspond to 1/r^2.

The hairy ball theorem is an interesting point. Maybe to equate particles with
vortices we have to work in 4d spacetime, since that theorem only applies to
even-dimensional spheres?

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mrcactu5
here's a nice answer on MathOverflow

[http://mathoverflow.net/questions/251470/topology-and-
the-20...](http://mathoverflow.net/questions/251470/topology-and-
the-2016-nobel-prize-in-physics/)

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nojvek
Can anyone tldr this paper?

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T-A
Try the pop version. It's not even 5 pages:

[https://www.nobelprize.org/nobel_prizes/physics/laureates/20...](https://www.nobelprize.org/nobel_prizes/physics/laureates/2016/popular-
physicsprize2016.pdf)

