Friday, May 21, 2010

Illustrating broken symmetry

Broken symmetry is one of the most important concepts in theoretical physics. It can be illustrated in a very simple way:

Consider four cities, each is located at a corner of a square.

Find the shortest possible way to join the cities by segments of straight roads.
One possible (non-optimum) solution is just lines along three sides of the square.

Allow for more than one possible optimum solution.
Does your solution maintain the four-fold symmetry of the original square?

I use this example (which I first heard from my Ph.D advisor, Jim Sauls, in his first lecture in a graduate class on condensed matter).

I now give it in an undergraduate course on thermodynamics of condensed matter. Here is a draft of the lecture for monday.
It is one of my favourite because it also discusses space shuttle experiments and shows some cool videos involving broken symmetry in soap films.

1 comment:

  1. Hmm. I just tried looking at the solution to the four city problem, but the Google Docs version of the presentation doesn't show the lines :(

    Just by intuition, I'd assume the solution looks like a letter Y above an upside down letter Y.