Picking up the trail

After this brief excursion into the world of the large, let us descend again into the quantum realm. In the following chapters I will try to bring together the main elements of the story, namely relativity, quantization and symmetry. We have seen how the first two lead to a picture of the subatomic world in which quanta are constantly exchanged between vertices in space-time. These quanta can be divided into two groups, the fermions and the bosons, which obey the Law of Spin and Statistics. One of the consequences of this law is the identification of fermions with matter and bosons with forces. We also saw that relativity and the boson–fermion classification can be attributed to certain regularities in the behaviour of space and time, called symmetries: conservation of angular momentum is tied to the fact that space does not change when it is rotated; the laws of relativity and the law of spin and statistics are consequences of the fact that space-time does not change when it is subjected to a Lorentz rotation.

It remains for me to argue that such symmetries are the all-encompassing organizing principle in the Universe, in the sense that they dictate the way in which fermions and bosons are coupled at a vertex. Thus, symmetries provide the final link in the story, because they prescribe the relationship of matter and forces.