{"id":983,"date":"2023-07-06T15:25:44","date_gmt":"2023-07-06T20:25:44","guid":{"rendered":"http:\/\/www.fruechtetheory.com\/blog\/?p=983"},"modified":"2023-07-06T15:35:28","modified_gmt":"2023-07-06T20:35:28","slug":"polarization-factor","status":"publish","type":"post","link":"https:\/\/www.fruechtetheory.com\/blog\/2023\/07\/06\/polarization-factor\/","title":{"rendered":"Polarization Factor"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">It has been said that the Coulomb field transmits by torsion and centrifugal force:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.fruechtetheory.com\/blog\/2023\/01\/29\/magnetic-fields-as-effecting-coulomb-groups\/\">https:\/\/www.fruechtetheory.com\/blog\/2023\/01\/29\/magnetic-fields-as-effecting-coulomb-groups\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.fruechtetheory.com\/blog\/2022\/03\/29\/transmission-of-the-coulomb-field\/\">https:\/\/www.fruechtetheory.com\/blog\/2022\/03\/29\/transmission-of-the-coulomb-field\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In the near field of molecules there are van der Waals attractive forces \u201cproportional to 1\/r<sup>7<\/sup>.\u201c ([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.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Kobayashi and Nomizu put it this way:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201cTheorem 2.2.&nbsp; <em>Every Riemannian manifold admits a unique metric connection with vanishing torsion<\/em>.\u201d ([2], pg. 158)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Additionally, there is an \u201cinvariant Riemannian metric which is naturally reductive\u201d. ([3], pg. 377)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">It has been said before that gauge invariance is local at a given time. When it is referred to as a \u201cunique metric connection\u201d, the instantaneous density of the gravitational field at an area of the surface of any planet is unique.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">One reason the potential energy of a point charge is not infinite was given here:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.fruechtetheory.com\/blog\/2009\/03\/15\/electric-charges\/\">https:\/\/www.fruechtetheory.com\/blog\/2009\/03\/15\/electric-charges\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In real time, the polarization factor is the reason the potential energy of a point charge is not infinite.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[1] Tipler, Paul A. and Llewellyn, Ralph A., \u201cModern Physics Sixth Edition\u201d, W.H. Freeman and Company, New York, c. 2012<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[2] Kobayashi, Shoshichi and Nomizu, Katsumi, \u201cFoundations of Differential Geometry Volume I\u201d, John Wiley &amp; Sons, Inc., c. 1963<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[3] Kobayashi, Shoshichi and Nomizu, Katsumi, \u201cFoundations of Differential Geometry Volume II\u201d, John Wiley &amp; Sons, Inc., c. 1969<\/p>\n","protected":false},"excerpt":{"rendered":"<p>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 \u201cproportional to 1\/r7.\u201c ([1], pg. 390) This is a fast reduction, in part due to the polarization factor, which is very strong, though not as strong [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,7,18],"tags":[],"class_list":["post-983","post","type-post","status-publish","format-standard","hentry","category-astrophysics","category-classical-electrodynamics","category-mathematics"],"_links":{"self":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/983","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/comments?post=983"}],"version-history":[{"count":3,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/983\/revisions"}],"predecessor-version":[{"id":986,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/983\/revisions\/986"}],"wp:attachment":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/media?parent=983"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/categories?post=983"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/tags?post=983"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}