T

he mathematics of Bose and Fermi statistics are well understood but there is no 'geometric rationale' acting as a foundational 'form' which is a requirement of the fundamental postulate. (see Internalization of Logic)
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.
Probability fields are attractive when the isotropic (determinate, absolute) grid is the standard and repulsive when the positional (indeterminate. relativistic) field is the standard.

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).
This is equivalent to repulsion.

[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 Possibilities

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

• Bosons - the N and X forms remain invariant through the "obscura" (though the N form can show a "hand"). Hence, only integral spins are possible, i.e. since the structure is the same at each wave it must have come around 0,1,2,3 ... times to be in such a state.
• Fermions - the TLC forms are rotated 180^o with the L form displaying handedness. Hence, they may represent 1/2 integral spins only (1/2, 3/2, 5/2 ...) Also, T and C forms may be logically the same for present purposes.

(Note: One could recalibrate and call them odd & even also. Bosons - 0,2,4 ... Fermions - 1,3,5 ... )
I do not presently (6/28/98) know what the connection is between integral / half-integral and attraction-repulsion. Nor do I know of any mechanism for generating any subatomic particles beyound electron, proton, neutron.