{"id":1018,"date":"2023-10-27T12:41:44","date_gmt":"2023-10-27T17:41:44","guid":{"rendered":"https:\/\/www.fruechtetheory.com\/blog\/?p=1018"},"modified":"2023-10-27T15:09:59","modified_gmt":"2023-10-27T20:09:59","slug":"pauli-exclusion-principle","status":"publish","type":"post","link":"https:\/\/www.fruechtetheory.com\/blog\/2023\/10\/27\/pauli-exclusion-principle\/","title":{"rendered":"Pauli Exclusion Principle"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">With the Pauli exclusion principle, \u201cOnly two electrons (with opposite spins) can occupy a given quantum state.\u201d ([1], pg. 798) The magnetic moments being in opposite directions help keep the separation, though it is electric current loops in each electron doing the work.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ref: <a href=\"https:\/\/www.fruechtetheory.com\/blog\/2022\/02\/14\/spin-drive\/\">https:\/\/www.fruechtetheory.com\/blog\/2022\/02\/14\/spin-drive\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The reason orbitals in an atom or molecule are limited to two electrons has to do with the fact that \u201c\u03c3, \u03c4 are any (local) bisections of G\u201d. ([2], pg. 28) In mechanical engineering, \u03c3 is the symbol for stress. Likewise, \u03c3 is the symbol here for local negative charge stress in the gamma ray field, and we have \u201cThe map \u03c6: \u03c3 \u2192 \u03b3\u201d ([3], pg. 226). Alternatively, there is \u201cthe sheaf of germs of local bisections of G.\u201d ([2], pg. 133) Here we have another name for the graviton in \u201cgerm\u201d, and a \u201csheaf\u201d is a member of the h field, when two or more gravitons get combined to do the work.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">With the spin of the electron, \u201cthe mapping S<sub>\u03c3<\/sub> \u2192 a<sub>\u03c3<\/sub><sup>n<\/sup> S<sub>\u03c3<\/sub>\u201d ([4], pg. 162) provides a matrix theory to the Coulomb field, with \u201ccyclic groups (\u03c3<sub>i<\/sub>) of orders n<sub>i<\/sub>\u201d ([4], pg. 130). This provides additional proof that Coulomb groups are pulsed.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Two other authors call the Pauli exclusion principle a \u201cset of pairs (\u03c4, J)\u201d ([5], pg. 68), with \u201cpermutations \u03c3\u201d ([6], pg. 293). J is a charged mass:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.fruechtetheory.com\/blog\/2023\/06\/29\/vector-bosons-and-other-fleeting-field-particles\/,\">https:\/\/www.fruechtetheory.com\/blog\/2023\/06\/29\/vector-bosons-and-other-fleeting-field-particles\/,<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">and in this case we are referring to an electron.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Physicists already knew most of this blog entry before it was entered. What many people do not know is the presence of a gamma ray field, though it is reasonable to know because of the gamma ray telescopes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[1] Tipler, Paul A., \u201cPhysics\u201d, Worth Publishers, Inc., 1976<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[2] 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\">[3] Bishop, Richard L. and Crittenden, Richard J., \u201cGeometry of Manifolds\u201d, AMS CHELSEA PUBLISHING, Copyright 1964 held by the American Mathematical Society. Reprinted with corrections by the American Mathematical Society, 2001<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[4] Zassenhaus, Hans J., \u201cTHE THEORY OF GROUPS\u201d, Dover Publications Inc., 1999 (Originally published by Chelsea Publishing Co., 1958)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[5] 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\">[6] 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>With the Pauli exclusion principle, \u201cOnly two electrons (with opposite spins) can occupy a given quantum state.\u201d ([1], pg. 798) The magnetic moments being in opposite directions help keep the separation, though it is electric current loops in each electron doing the work. Ref: https:\/\/www.fruechtetheory.com\/blog\/2022\/02\/14\/spin-drive\/ The reason orbitals in an atom or molecule are limited [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7,18,16],"tags":[],"class_list":["post-1018","post","type-post","status-publish","format-standard","hentry","category-classical-electrodynamics","category-mathematics","category-quantum-field-theory"],"_links":{"self":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/1018","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=1018"}],"version-history":[{"count":2,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/1018\/revisions"}],"predecessor-version":[{"id":1020,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/1018\/revisions\/1020"}],"wp:attachment":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/media?parent=1018"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/categories?post=1018"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/tags?post=1018"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}