Consider a particle P, that is described by the coefficients of its rotating seeds and . We say that P has a spin that is defined by these coefficients, as noted in the accompanying table. We also use the helicity, written as
to make quantitative descriptions of P’s spatial orientation. And later, if P is also being used as a frame of reference, then and may be used to establish the phase of other particles. So rotating seeds have an important role in describing motion. This task is expanded by considering the coefficients of leptonic seeds, , , and , to define
where is the electric polarity and is the magnetic polarity. Then we specify the total angular momentum vector as . Exchanging quarks for anti-quarks does not alter seed counts, so In general, the components , and have non-zero values, and P’s motion is complicated. But for a solitary, undivided particle that is not electrically or magnetically polarized we may construct a framework where P is centered on the electric and magnetic axes. Then it is easy to assess the norm of because and . The vector is aligned with the polar-axis, and so
This expression is simplified by defining the total angular momentum quantum number as
Total Angular Momentum is Conserved
If then the -component of the angular momentum vector can be expressed in terms of as
And if then the radical is approximately one, and
Similar results obtain for the other axes so that
But seeds are conserved, so the quantity and character of the seeds in a description cannot change. Whenever some generic compound quarks , and interact, if then the coefficients for any sort of seed Z are related as
Then by the associative properties of addition, the angular momentum must be approximately conserved too. For macroscopic particles, is huge because is so small, and the approximation is excellent.
Rotating seeds are objectified from achromatic visual sensations, so for spin-up particles, white sensations outnumber black sensations. Collectively they are bright. For spin-down particles, black sensations are more numerous than white sensations, they look dark. Non-rotating particles are in between, they are greyish. So indicates if a complex achromatic visual sensation is brighter or darker than some medium grey visual experience. And notes the size of the difference.