Mar 19 2024

## Spherical Groups

With spherical groups of opposite charge signs, like emitted by the proton and electron in hydrogen, why would they not annihilate each other at different spots? For one thing they are segmented and pulsed, and spread out, and come out of a charged mass in pairs. These are convex regions, and “A region *X* open or closed, will be called convex if any two points in *X* are joined by at least one path which does not leave *X*.” ([1], pg. 7)

Additionally, “Let X be any open region and *Ⴟ* its closure.” ([1], pg. 7) It is like the groups have AI, and know how to avoid each other and know how to come back together. In footnote “*” on page 7, attributed to K. Menger, “We may think of *X* as filled with substance which conducts light along paths, all the space except *X* being opaque.”

At least in atoms or molecules, at close range, the groups are strong enough to avoid each other, before the polarization factor takes over. As far as hitting a target, the Coulomb field travels at the speed of light squared, and more groups come through fast.

[1] Whitehead, J. H. C., “CONVEX REGIONS IN THE GEOMETRY OF PATHS”, Princeton Press, (Received 15 August 1931)

on 25 Mar 2024 at 10:36 amAs far as vector potential groups traveling through the open gamma ray field, “Cartan made a systematic use of the “fundamental quadratic form” of g” ([2], pg. 6]. With the Coulomb field traveling at the speed of light squared, the units are m^2/s^2. The s^2 in the denominator has to do with gravitational acceleration.

[2] SHIING-SHEN CHERN AND CLAUDE CHEVALLEY, “ELIE CARTAN AND HIS MATHEMATICAL WORK”, Amer. Math. Soc., March 1952