对称性破缺

今年的诺贝尔物理奖涉及的问题是对称破缺，John Armstrong在Mark C. Chu-Carroll的博客上举了两个对称性破缺（symmetry-breaking）的简单例子：

The canonical example to define symmetry-breaking is a bunch of people seated around circular table. Each place setting has a plate, and there's a cup set between each pair of plates. The situation has a rotational symmetry (turn by one setting) and a reflection symmetry (draw a line across the center of the table, through a pair of plates).

But is the cup on your right side or your left side part of your setting? When everyone sits down, it doesn't matter, since everything is symmetric. But if I grab the cup on my right, the woman sitting there has to grab the cup on her right, and the man on the other side has to grab the cup on his right, and so on all round until we get to the woman on my left who grabs the cup on her right -- my left.

Now the reflection symmetry has been broken, but the rotational symmetry remains.

另一个例子是：

It strikes me I should say something about spontaneous symmetry-breaking.
The canonical example here is to consider a punted wine bottle. That is, the bottom isn't flat, but is domed up in the middle. It's rotationally symmetric. If you place a marble on the punt in the exact center, it will balance and the situation is still symmetric.

But that situation isn't stable. The slightest nudge will push the marble off the center (just like one person grabbing the left or the right cup). Then it will roll off in that directly until it comes to rest in the groove at the base of the punt. Now the rotational symmetry has been broken, since one direction from the center has been identified as different.

The important thing is that nobody made a "choice" here. Energetically, the non-symmetric configurations are all just as good as each other, but they're all better than the symmetric position. So the tendency of the universe to minimize energy is what "spontanously" breaks the symmetry without having to "intentionally" break it by making a choice to pick out one direction over the others.