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I can follow the matrix algebra (just!) which gives rise to right and left handed spinors; that they Lorentz transform differently but this is just theory. Surely an electron is an electron. I understood them to have spin up or down = ± ħ / 2 from my undergraduate QM studies but this concept of differences in isospin and other quantum numbers has thrown me.

Can anyone shed some light on the reason behind these differences in a relatively non-mathematical way?