(Assembled from disclosures made by space people in various communications.)
We have had a superficial look at the behaviors of a single spin center and a peek at a multiplicity of spin centers. We know that our matter is made up of enormous numbers of spin centers, some of which are relatively quite close together, so let us now see what happens when there are a great many to consider.
In the first place, all the spin centers could be lined up; that is, their spin vectors could all be pointing in the same direction. In this case we would say that such matter is "polarized", and we would expect different properties than from unpolarized matter in which the spin vectors were randomly oriented.
It may be readily appreciated that at any point the effect of the summation of each of the fields due to each individual spin will depend on (a) the relative distance from the reference point to each spin center, and (b) the relative orientation of the spin centers with respect to one another. This consideration is apart from any "background" field that may be present.
Since spin is both scalar and vector, it follows that the scalar components will simply add up, while the laws of vector addition will be followed by the vector components, with one important additional consideration. The scalar addition must be performed before the mathematical operations with del are performed to yield the field conditions. This consideration is merely stated at this stage as being important. Its significance will be apparent later, but it has to do with the fact that spin, which is what is being operated upon, is in itself the only absolute quantity with respect to which the operation may be performed.
Another important consideration is to realize that spin centers are exactly what their name implies; they are centers about which the units of reality function. They are not particles. Therefore, the standard equations of vector analysis such as LaPlace's and Poisson's equations may not always be valid. These equations are derived on the assumption that the entire virtue of a particle is contained within the point center and its only influence is apparent outside of the point. This is of course not the case, as the entire virtue of a spin center actually lies completely outside the point center, and may correctly be said to be everywhere except within the point.