{"id":35,"date":"2008-02-14T20:11:07","date_gmt":"2008-02-15T01:11:07","guid":{"rendered":"http:\/\/www.fruechtetheory.com\/blog\/2008\/02\/14\/half-integer-spin-contribution\/"},"modified":"2008-03-22T10:20:12","modified_gmt":"2008-03-22T15:20:12","slug":"half-integer-spin-contribution","status":"publish","type":"post","link":"https:\/\/www.fruechtetheory.com\/blog\/2008\/02\/14\/half-integer-spin-contribution\/","title":{"rendered":"Half-integer spin contribution"},"content":{"rendered":"<p><font size=\"2\">With the emission of a graviton, an electron in an atomic quantum orbit must either undergo a nutation, or reverse its spin orientation as it contributes to the particle angular momentum.<br \/>\n<\/font><font size=\"2\">The shape of an orbital that you see at the top of this blog is similar to what many of us picture, however reality may be something different.\u00a0 Let us say, for discussion purposes, that an electron reverses its spin orientation when it gives off a graviton.\u00a0 The electron as a particle with half-integer spin changes sign \u201cwhen the system of coordinates is completely rotated about an axis\u201d ([1], \u00a754). \u00a0\u00a0Should each orbital then include graviton emitting turns of quantity 2n+1, n=1,2,3, the spin orientation of the electron would reverse for every course that brings it back to its orientation and position relative to starting coordinates within d(q-q\u2019).\u00a0 The total particle angular momentum will then alternate along any prescribed axis between <em><font face=\"Times New Roman\">j<\/font><\/em> = <em><font face=\"Times New Roman\">l<\/font><\/em> + \u00bd and <em><font face=\"Times New Roman\">j<\/font><\/em> = <em><font face=\"Times New Roman\">l<\/font><\/em> \u2013 \u00bd.<br \/>\n<\/font><font size=\"2\">Another way of stating it is that for half-integer <em><font face=\"Times New Roman\">j<\/font><\/em>, <em>\u03a7<\/em>(<em>\u0424<\/em>+2\u03c0) = &#8211;<em> \u03a7<\/em> (<em>\u0424<\/em>).\u00a0 The base function changes sign under a rotation of 2\u03c0 ([1], \u00a795).<br \/>\n<\/font><font size=\"2\">It is the statistical nature of quantum mechanics that has allowed its angular momentum and energy eigenvalue determinations to be very useful in physics.\u00a0 The average intrinsic spin angular momentum of the electron has thus been able to be used without respect to the emission and absorption of gravitons.<br \/>\n<\/font><font size=\"2\">\u00a0<\/font><\/p>\n<p><font size=\"2\">[1] Landau, L. D. and Lifshitz, E. M., <u>Quantum Mechanics, Non-relativistic Theory<\/u>, Translated from the Russian by J. B. Sykes and J. S. Bell, Addison-Wesley Publishing, 1958<\/font><\/p>\n","protected":false},"excerpt":{"rendered":"<p>With the emission of a graviton, an electron in an atomic quantum orbit must either undergo a nutation, or reverse its spin orientation as it contributes to the particle angular momentum. The shape of an orbital that you see at the top of this blog is similar to what many of us picture, however reality [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-35","post","type-post","status-publish","format-standard","hentry","category-quantum-mechanics"],"_links":{"self":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/35","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=35"}],"version-history":[{"count":0,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/35\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/media?parent=35"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/categories?post=35"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/tags?post=35"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}