For non-expert readers who want to dig a bit deeper. This is the first post of two, the second of which will appear in a day or two:
In my last post I described, for the general reader and without using anything more than elementary fractions, how we know that each type of quark comes in three “colors” — a name which refers not to something that you can see by eye, but rather to the three “versions” of strong nuclear charge. Strong nuclear charge is important because it determines the behavior of the strong nuclear force between objects, just as electric charge determines the electric forces between objects. For instance, elementary particles with no strong nuclear charge, such as electrons, W bosons and the like, aren’t affected by the strong nuclear force, just as electrically neutral elementary particles, such as neutrinos, are immune to the electric force.
But a big difference is that there’s only one form or “version” of electric charge: in the language of professional physicists, protons have +1 unit of this charge, electrons have -1 unit of it, a nucleus of helium has +2 units of it, etc. By contrast, the strong nuclear charge comes in three versions, which are sometimes referred to as “redness”, “blueness” and “greenness” (because of a vague but highly imprecise analogue with the inner workings of the human eye). These versions of the charge combine in novel ways we don’t see in the electric context, and this plays a major role in the protons and neutrons found in every atom. It’s the math that lies behind this that I want to explain today; we’ll only need a little bit of trigonometry and complex numbers, though we’ll also need some careful reasoning.