Hi folks, I was just reading about symmetries, and why we say that the two spin states of the electron are states of the same particle, while we are free to say that the two strong isospin states define tow different types of particle. According to the book I'm reading, we must attribute two spin states to one and the same particle because the dynamics can distinguish between states of different spin (the triplet state having a different energy than the singlet state, for example). But that made me think: what about color? We say that e.g. each quark has 3 color states, but can be the dynamics distinguish between these states? Any thoughts much appreciated!
The book is blowing smoke at you. The real reason is that strong isospin isn't an exact symmetry so particles related to each other through an isospin transformation will have different properties. The neutron is heavier than the proton and doesn't have a charge, for instance
Well, to be fair the book was stating how things looked from the perspective of strong-interaction theory alone (so no EM charge yet). And it doesn't seem so crazy: for consider the following. Given that particle dynamics is sensitive to spin, we can dynamically distinguish between the spin-up and spin-down states of a given particle: these two states are eigenstates of Sz. Then we can define a spin-flip operator, Sx, which relates these physically distinct states to one another and as such can be seen as a real physical operation (instead of just a piece of mathematical formalism). But then since Sx is a real physical operator, we must be able to ascribe physical states of Sx to the particle we started with; but then these will be superpositions of the Sz eigenstates (owing to the non-commutativity), so that we must be able to ascribe both spin states to the same particle (insofar as that's exactly what the superposition says is going on). So it seems that where the dynamics can distinguish between two states, we *must* be able to ascribe each of those states to one and the same particle, and hence we cannot that each state denotes a different particle. My question is then just this: one what grounds do we say that there are 3 states to each of the 6 quarks, not 3x6 different types of quark? Do the QCD dynamics distinguish the three states, or not?
My answer is the same it was before. What we decide to call different states of a particle and what we decide to call different particles is somewhat arbitrary. The (left handed) electron and the neutrino are related to each other by a weak isospin transformation and we call them separate particles. That's entirely equivalent to the fact that a blue-up quark is related to a red-up quark by a color transformation and we call them two states of a single particle. Why? well the weak isospin is spontaneously broken and the color symmetry isn't, so electrons and neutrinos acquire different properties. There is nothing particularly fundamental about that choice.