Poisson equation solutions differ for classical and neoclassical formulations of the associated boundary value problem only to the extent that the distance scale factor is zero for the classical situation. So this fragmentation issue applies to both alternatives since the effect is independent of the scale factor.
If a Poisson distribution solution were to somehow be divided into n equal sub-distributions of identical total charge or mass and scale factor, the total energy of the n resulting distributions would be reduced to 1/n of the energy in the original distribution. The fragmentation phenomena would disperse the n identical electric charges by their repulsive force out to infinity. However, for a gravitational mass fragmentation would result in the n masses collapsing back onto each other, thereby reducing energy since the gravitational energy is negative. This is why stable fundamental particle distributions of a given total energy mass depend upon both aspects for indivisibility. That the electric charge and mass of a subatomic particle should be inextricably linked is no surprise; that is the essence of an ‘indivisible particle’. We will discuss this bipartite linkage next time.
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