Structure of space due to the relativistic “smearing” of a point charge

Conclusions

• 1. The “smearing” of a point charge required by the theory of relativity can be explained in terms of a transition from a continuum to a discrete space with a statistical size distribution of cells.

• 2. A relation has been found between the density of this distribution and the volume density of the smeared charge under the assumption that each cell of the space is uniformly filled by a charge of the same magnitude.

• 3. For the repulsive case, the distribution density is reminiscent of a δ-function, becoming infinite at r = r₀ and vanishing at r = 0 and r = ∞; for the attractive case, on the other hand, the distribution has three zeros (in certain cases, the first two zeros merge). The charge filling the small cells has the sign opposite that of the charge filling the large cells.