Symmetry Breaking

In the last chapter, we illustrated some of the power of symmetries in solving puzzles, in studying physics and in the world and universe around us. We noted that symmetries are equivalent to conservation laws in physics and conservation laws, as you may have noticed, can be very useful. One basic application, as we saw in the puzzle with the cards, is that if things do not add up, we then know something is missing, and we can get information about the missing thing by counting what is, and is not, there. In this chapter we discuss the opposite concept: situations where symmetries are broken. And you may be surprised to find out that, in some cases, these broken symmetries can be more interesting and consequential in nature than unbroken ones.