The Meaning of Symmetry

Abstract

We are fundamentally discussing a question of language: what we now call symmetry. But questions of language are not unimportant. After all, we want to communicate with each other. In physics, the word symmetry has been used, in my opinion, in three different senses. I will try to describe them and tell you why I do not like the idea of gauge invariance being a symmetry principle. But perhaps I am wrong and I will be contradicted. Well, in the ordinary sense, symmetry means symmetry of objects, mainly of crystals. You know that there are 32 crystal classes, 230 space groups; and you know that crystals have remarkable symmetries even though the symmetry is not usually quite as good as it is postulated. But the internal structure obeys the principle of symmetry really amazingly well, and if we were not discussing a very general question, I would have gone into more details of this because there are many interesting things that can be said about it. This is the first concept of symmetry, just a symmetry of objects.