Which hand is right?
So the fact of the matter is that in studying any phenomenon there are always two right-hand rules, or an even number of them, and the net result is that the phenomena always look symmetrical. In short, therefore, we cannot tell right from left if we also are not able to tell north from south. However, it may seem that we can tell the north pole of a magnet. The north pole of a compass needle, for example, is one that points to the north. But of course that is again a local property that has to do with geography of the earth; that is just like talking about in which direction is Chicago, so it does not count. If we have seen compass needles, we may have noticed that the north-seeking pole is a sort of bluish color. But that is just due to the man who painted the magnet. These are all local, conventional criteria. However, if a magnet were to have the property that if we looked at it closely enough we would see small hairs growing on its north pole but not on its south pole, if that were the general rule, or if there were any unique way to distinguish the north from the south pole of a magnet, then we could tell which of the two cases we actually had, and that would be the end of the law of reflection symmetry. To illustrate the whole problem still more clearly, imagine that we were talking to a Martian, or someone very far away, by telephone. We are not allowed to send him any actual samples to inspect; for instance, if we could send light, we could send him right-hand circularly polarized light and say, “That is right-hand light—just watch the way it is going.” But we cannot give him anything, we can only talk to him. He is far away, or in some strange location, and he cannot see anything we can see. For instance, we cannot say, “Look at Ursa major; now see how those stars are arranged. What we mean by ‘right’ is …” We are only allowed to telephone him. Now we want to tell him all about us. Of course, first we start defining numbers, and say, “Tick, tick, two, tick, tick, tick, three, …,” so that gradually he can understand a couple of words, and so on. After a while we may become very familiar with this fellow, and he says, “What do you guys look like?” We start to describe ourselves, and say, “Well, we are six feet tall.” He says, “Wait a minute, what is six feet?” Is it possible to tell him what six feet is? Certainly!  We say, “You know about the diameter of hydrogen atoms—we are $17{,}000{,}000{,}000$ hydrogen atoms high!” That is possible because physical laws are not invariant under change of scale, and therefore we can define an absolute length. And so we define the size of the body, and tell him what the general shape is—it has prongs with five bumps sticking out on the ends, and so on, and he follows us along, and we finish describing how we look on the outside, presumably without encountering any particular difficulties. He is even making a model of us as we go along. He says, “My, you are certainly very handsome fellows; now what is on the inside?” So we start to describe the various organs on the inside, and we come to the heart, and we carefully describe the shape of it, and say, “Now put the heart on the left side.” He says, “Duhhh—the left side?” Now our problem is to describe to him which side the heart goes on without his ever seeing anything that we see, and without our ever sending any sample to him of what we mean by “right”—no standard right-handed object. Can we do it?