{"id":1010,"date":"2023-10-16T19:56:14","date_gmt":"2023-10-17T00:56:14","guid":{"rendered":"https:\/\/www.fruechtetheory.com\/blog\/?p=1010"},"modified":"2023-11-12T11:49:07","modified_gmt":"2023-11-12T16:49:07","slug":"atomic-and-molecular-electron-arcs","status":"publish","type":"post","link":"https:\/\/www.fruechtetheory.com\/blog\/2023\/10\/16\/atomic-and-molecular-electron-arcs\/","title":{"rendered":"Atomic and Molecular Electron Arcs"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Further to uniting Riemannian geometry, Lie groups, and symmetric spaces with gravity, \u03c4 is an atomic or molecular arc, and \u201c\u03c4 is a segment\u201d ([1], pg. 168). Also, \u201c\u03c4 is minimizing\u201d ([1], pg. 166).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sometimes \u03c4 is called a complete orbital, and we \u201cdivide \u03c4 into a finite number of arcs, say, \u03c4<sub>1<\/sub>, \u03c4<sub>2<\/sub>, \u2026 , \u03c4<sub>k<\/sub>\u201d ([1], pg. 191).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ref: <a href=\"https:\/\/www.fruechtetheory.com\/blog\/2008\/06\/28\/gravity-and-the-uncertainty-principle-2-2\/\">https:\/\/www.fruechtetheory.com\/blog\/2008\/06\/28\/gravity-and-the-uncertainty-principle-2-2\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In an orbital arc the \u201cendomorphisms A<sup>1<\/sup>, \u2026 , A<sup>k<\/sup> are linearly independent\u201d ([2], pg. 353), and k \u2013 1 in this instance is the number of gravitons absorbed in an arc. \u201cA\u201d is the vector potential, and each time an electron absorbs a graviton in an orbital, its vector potential increases. We know that A<sup>1<\/sup>, \u2026 , A<sup>k<\/sup> is not pulsed Lie groups in the gamma ray field, because there is no \u201c\u2026\u201d after the A<sup>k<\/sup>. In the same paragraph it talks about a \u201cmapping \u03be \u2192 A<sub>\u03be<\/sub>\u201c, therefore in a particle mass, and in groups or manifolds in the open gamma ray field, the gamma rays are blended and surjective.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If a function can be called \u201cthe growth of an orbital electron in size and charge\u201d:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.fruechtetheory.com\/blog\/2022\/08\/27\/concentrated-group-action\/\">https:\/\/www.fruechtetheory.com\/blog\/2022\/08\/27\/concentrated-group-action\/<\/a> ,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">then \u201c\u03b3 and f point in opposite directions\u201d ([3], pg.165).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The \u03a6 field is within atomic and molecular orbitals, including the boundary, and \u03a8 is outside of the orbitals. In an emitting antenna, it is the \u03a8 field as well, since the electrons are free. \u201c\u03a6<sup>0<\/sup> is isomorphic to \u03a8<sup>0<\/sup> in a natural manner\u201d ([1], pg. 193), because the gamma ray field is normally constant in the area within and around the molecule.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Often in a molecule, or any type of p orbital, the Gaussian curvature, when \u00be through the arc compared to \u00bc through the arc, is negative.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In the open gamma ray field \u201cm = dim M and n = dim \u0394\u201d ([4], pg. 155), and m \u2013 n is the number of singularities in a locality. Stoker terms it \u201csingularity in the coordinate system\u201d ([5], pg. 84). A singularity is when the electric and magnetic fields of a gamma ray cross over the t axis, though when near the axis it could be called a singularity also.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If the polarization factor is greater than 2, as at the surface of the sun or Jupiter, then specific nuclei likely have more mass than on the face of the earth, and electrons in atomic or molecular arcs grow larger. It could be because of these factors the value of Newton\u2019s gravitational constant G = 6.672 x 10<sup>-11<\/sup> (N-m<sup>2<\/sup>)\/ kg<sup>2<\/sup> stays the same.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[1] 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\">[2] Kobayashi, Shoshichi and Nomizu, Katsumi, \u201cFoundations of Differential Geometry Volume II\u201d, John Wiley &amp; Sons, Inc., c. 1969<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[3] Mackenzie, Kirill C. H., \u201cGeneral Theory of Lie Groupoids and Lie Algebroids\u201d, c. 2005 Kirill C. H. Mackenzie, London Mathematical Society<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[4] Boothby, William M., \u201cAn Introduction to Differentiable Manifolds and Riemannian Geometry\u201d, Academic Press, 2003<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[5] Stoker, James J., \u201cDifferential Geometry\u201d, John Wiley &amp; Sons, Inc., c. 1969<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Further to uniting Riemannian geometry, Lie groups, and symmetric spaces with gravity, \u03c4 is an atomic or molecular arc, and \u201c\u03c4 is a segment\u201d ([1], pg. 168). Also, \u201c\u03c4 is minimizing\u201d ([1], pg. 166). Sometimes \u03c4 is called a complete orbital, and we \u201cdivide \u03c4 into a finite number of arcs, say, \u03c41, \u03c42, \u2026 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,11,10,16,20],"tags":[],"class_list":["post-1010","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-newtonian-mechanics","category-nuclear-physics","category-quantum-field-theory","category-string-theory"],"_links":{"self":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/1010","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=1010"}],"version-history":[{"count":5,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/1010\/revisions"}],"predecessor-version":[{"id":1034,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/1010\/revisions\/1034"}],"wp:attachment":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/media?parent=1010"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/categories?post=1010"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/tags?post=1010"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}