# What does Bell mean by polarization of spin state?

I am reading John Bell's article On the Einstein Podolsky Rosen paradox and I am confused by the following sentence in the beginning of part III:

Suppose we have a spin half particle in a pure spin state with polarization denoted by a unit vector ...

What does Bell mean by polarization of spin $$\tfrac12$$ state?

• Spin has a direction. If spin is polarized it just means the spin points along a particular direction. Jun 4 at 5:43
• @josephh how spin can be not polarized? Jun 4 at 7:00
• Because you need a direction along with the spin orientation. You cannot say that because a particle has spin direction, then it's automatically polarized. In this instance, the particle spin is polarized along the direction denoted by the unit vector. Jun 4 at 7:06
• @josephh Well, you confused things completely. What is spin orientation? Spin can be measured along any orientation. How it differs from spin polarization? Jun 4 at 7:23
• The particles are prepared in such a way that a spin measurement will always reveal a spin parallel to the unit vector. This is called "polarization." Jun 5 at 2:42

The space of states of a spin-1/2 object is the Bloch sphere, which, as the name implies, can be viewed as the two-sphere $$S^2\subset\mathbb{R}^3$$. Every point of the sphere corresponds to a unit vector $$\hat{n}\in\mathbb{R}^3$$, and the state corresponding to it is an eigenstate of the spin operator $$S_{\hat{n}}$$ that measures the spin in that direction. This $$\hat{n}$$ is the "polarization vector".