Does spin measurement yield discrete values or continuous outcomes?

[andrewkirk]

I am trying to understand the measurement of spin, in order to understand Bell's paper on the Einstein-Podolsky-Rosen paradox.

When we measure the spin of a fermion in the direction of unit vector a, will the result be:

1. a value of either +0.5 or -0.5, and upon measurement, the fermion adopts an eigenstate of the spin operator in which the spin is aligned with a

or

2. a value of 0.5 cos θ, where θ is the angle between a and the direction of spin the particle has adopted as a result of the measurement, and θ may be anywhere in [0, π)


or is it something else?

Thank you for any help.

 

[Bill_K]

1. a value of either +0.5 or -0.5, and upon measurement, the fermion adopts an eigenstate of the spin operator in which the spin is aligned with a

This one is correct.

 

[andrewkirk]

Thank you Bill.
I meant to say thanks earlier, but I got a bit carried away reading the Bell paper when I found I could actually understand it.