isospin symmetry
/ EYE-so-spin /
The proton and the neutron are oddly alike. They weigh almost exactly the same (the neutron is just 0.1 percent heavier), they are about the same size, and the strong nuclear force binds them into nuclei with near-total disregard for which is which. It is as if the strong force sees them not as two different particles but as two faces of a single object. Isospin is the bookkeeping that captures this near-twinhood.
The idea, borrowed by analogy from ordinary spin, is to treat the proton and neutron as a single particle — the nucleon — that comes in two 'isospin states', like an arrow that can point up (proton) or down (neutron). The strong force is then said to have isospin symmetry: it acts the same no matter how you 'rotate' between these states, just as ordinary physics does not care which way a spin points. In the quark picture the reason is plain: protons and neutrons differ only by swapping an up quark for a down quark, and the up and down quarks have very nearly the same mass and identical strong interactions. Isospin symmetry is really the statement that the up and down quarks are almost interchangeable as far as the strong force is concerned.
Isospin was historically crucial: it let physicists organize the growing 'zoo' of strongly interacting particles into tidy families — the three pions, for example, form an isospin triplet — and predict the existence and properties of particles before they were found. It is only an approximate symmetry, broken by the small mass difference between the up and down quarks and by electromagnetism (the proton is charged, the neutron is not). Later it was enlarged, by bringing in the strange quark, into the bigger SU(3) flavor symmetry behind the eightfold way.
The three pions — positively charged, negatively charged, and neutral — have nearly the same mass and behave as one isospin triplet, the three orientations of a single object under the strong force. Their tiny mass differences come almost entirely from electromagnetism, not the strong force itself.
The three pions form one isospin triplet under the strong force.
Isospin has nothing to do with real spin or rotation in space; it is an abstract 'internal' symmetry that just happens to use the same mathematics. It is also only approximate, broken by the up-down quark mass difference and electromagnetism.