I been reading some physics articles (related to the recent discovery of the particle that could be a Higgs boson) posted online and it was talking about electron spin and how it can only have values of either up or down and that always confused me. I know directions of up and down are really arbitrary because in just space there be no up and down. So unless spin orients itself depending on the nearest gravity source, spin of up/down must mean something different then in ordinary English language.
I also been confused by the fact that the article claims that you can have right/left spin as a result of a spin measurement:
Suppose you do measure an electron as spin up, and then try to measure the left-right spin. Common sense would tell you that that number would be zero, since you know that the electron is spin up, not left or right, but I warned you about common sense before. It turns out that a) half the time you'll measure the electron to be left and the other half you'll get right, and b) whether it's left or right is completely random.
I probably would understand what is meant by up/down spin if I knew how a spin of a particle is actually measured. (I think i could handle a detailed and precise explanation but a crude explanation will suffice if it gives insight to why spin is up or down and why it can come off as left and right in measurements)
Is up down just a name given by physicists to two different types of spins? Or does it have something to do with the actual directions?