Editing Four-vector (section)

===Four-spin===

The [[four-spin]] of a particle is defined in the rest frame of a particle to be
<math display="block">\mathbf{S} = (0, \mathbf{s})</math>
where {{math|'''s'''}} is the [[Spin (physics)|spin]] pseudovector. In quantum mechanics, not all three components of this vector are simultaneously measurable, only one component is. The timelike component is zero in the particle's rest frame, but not in any other frame. This component can be found from an appropriate Lorentz transformation.

The norm squared is the (negative of the) magnitude squared of the spin, and according to quantum mechanics we have
<math display="block">\|\mathbf{S}\|^2 = -|\mathbf{s}|^2 = -\hbar^2 s(s + 1)</math>

This value is observable and quantized, with {{math|''s''}} the [[spin quantum number]] (not the magnitude of the spin vector).