The following mechanism may underlie it.
The direction of the probability field is determined by the geometric field which physically acts as the standard of measure.
In the positional field, any collection of N particles or N trials will disperse to uniform distribution.
In this manner:
In the first trial 1/2 move toward the field origin
and 1/2 move away. Since 1/2 toward < 1/2 away (as
measured in the overall relativistic manifold), the
geometric center of N moves away from the origin (from the viewpoint of a standard observer).
[From the viewpoint of a purely relativistic reference frame (composed of positional fields only) a finite displacement away from an origin is always greater than the same displacement toward. Such a manifold is statistically compelled to disperse to uniform distribution as viewed by an observer in the normal reference frame.]
Conversely,when 1/2 toward = 1/2 away in the isotropic grid, 1/2 toward > 1/2 away (from the point of view of the positional field).
Spin PossibilitiesAll particles have a wave nature when in relative motion to any observer. As such they are subject to the manner of motion described in "Proposed Photon Experiment" (ntx18.htm).
Here, they must turn themselves upside down and rightside to left as their "innards" squeeze through what amounts to a camera obscura.
This process must be utterly fundamental if wavelike properties are to be employed in a geometric structure which does not spread out like ripples in a pond.
Of the five types of structures possible
(Note: One could recalibrate and call them odd & even also. Bosons - 0,2,4 ... Fermions - 1,3,5 ... )