Jul 06 2023
Polarization Factor
It has been said that the Coulomb field transmits by torsion and centrifugal force:
https://www.fruechtetheory.com/blog/2023/01/29/magnetic-fields-as-effecting-coulomb-groups/
https://www.fruechtetheory.com/blog/2022/03/29/transmission-of-the-coulomb-field/
In the near field of molecules there are van der Waals attractive forces “proportional to 1/r7.“ ([1], pg. 390) This is a fast reduction, in part due to the polarization factor, which is very strong, though not as strong as the Coulomb force of a concentrated charge of mass when another concentrated charge of mass is nearby.
Kobayashi and Nomizu put it this way:
“Theorem 2.2. Every Riemannian manifold admits a unique metric connection with vanishing torsion.” ([2], pg. 158)
Additionally, there is an “invariant Riemannian metric which is naturally reductive”. ([3], pg. 377)
It has been said before that gauge invariance is local at a given time. When it is referred to as a “unique metric connection”, the instantaneous density of the gravitational field at an area of the surface of any planet is unique.
One reason the potential energy of a point charge is not infinite was given here:
https://www.fruechtetheory.com/blog/2009/03/15/electric-charges/
In real time, the polarization factor is the reason the potential energy of a point charge is not infinite.
[1] Tipler, Paul A. and Llewellyn, Ralph A., “Modern Physics Sixth Edition”, W.H. Freeman and Company, New York, c. 2012
[2] Kobayashi, Shoshichi and Nomizu, Katsumi, “Foundations of Differential Geometry Volume I”, John Wiley & Sons, Inc., c. 1963
[3] Kobayashi, Shoshichi and Nomizu, Katsumi, “Foundations of Differential Geometry Volume II”, John Wiley & Sons, Inc., c. 1969