|MadSci Network: Physics|
Garr, You are right in saying that there is a spatial orientation to the electron's spin. However, the statement about the momentum should be clarified. When we talk about electon spin, we are talking about angular momentum, the momentum about a point in space. When we know the radius from this point to the object(s) moving about the point, and the mass and velocity of the object(s), then we can calculate the angular momentum of the system. For electrons, we do have a mass. However, we consider them to be point particles, so there is no value for a radius, so there is no way we can calculate velocity,( or frequency ), given the measured value for the angular momentum. The electron's spin is an intrinsic property of the electron as far as we know. The axis of the spin defines the direction, according to the right hand rule. If you have a vertically oriented spin for an electron that is spin up, and you drop the electron onto some object that absorbs the electron, that object will experience a torque in the counter clockwise direction when viewed from above. It turns out that the mathematical formalism developed for handling angular momentun (spin) is also quite useful in describing various other more abstract quantities in the quantum domain. When the formalism is adapted for use with such a quantity, people start talking about another new type of spin which may not have anything to do with angular momentum at all. One example is isospin, which is really just a bookkeeping thing that started out keeping track of proton and neutron interactions, and extends to help keep track of various other related particles. It views the proton and neutron as just "up" and "down" states of some more abstract nucleon object.
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