{"id":49,"date":"2008-04-01T13:22:36","date_gmt":"2008-04-01T18:22:36","guid":{"rendered":"http:\/\/www.fruechtetheory.com\/blog\/2008\/04\/01\/wave-function-transfer-2-2\/"},"modified":"2023-12-23T08:45:56","modified_gmt":"2023-12-23T13:45:56","slug":"wave-function-transfer-2-2","status":"publish","type":"post","link":"https:\/\/www.fruechtetheory.com\/blog\/2008\/04\/01\/wave-function-transfer-2-2\/","title":{"rendered":"Wave Function Transfer, Rev. A"},"content":{"rendered":"

The wave function of a free graviton can be written in the form
\n<\/span>E0<\/sub> sin (kx-\u03c9t) or B0<\/sub> sin (kx-\u03c9t)
\n<\/span>where the wave number k = p\/\u045b, and the electric and magnetic field components are in phase with each other.
\n<\/span>The momentum of a free graviton, which we will now call pg<\/sub> for purposes seen later, is written as pg<\/sub> = h\/\u03bbg<\/sub> = 1.671 x 10-19<\/sup> kg-m\/s. \u00a0The fundamental charge, termed e<\/em>, that of an electron or a proton, is 1.602 x 10-19<\/sup> C.\u00a0 Linear momentum from a free graviton must be transferred into angular momentum as it is absorbed by an electron in a quantum atomic orbital.
\n<\/span>In terms of energy, with the numerical value of pg<\/sub>2<\/sup>\/e<\/em>2<\/sup> at 1.088, generally we have
\n<\/span>pg<\/sub>2<\/sup>\/e<\/em>2<\/sup> = (Const.1<\/sub>) S<\/sub>\u222b B2<\/sup>\u2219n dA
\n<\/span>The rotational wave function of a graviton as an internal component of an electron may be of the form:
\n<\/span>\u03a8rot<\/sub> = (Const.2<\/sub>) exp [i2\u03c0\u03b1(e<\/em>B\/pg<\/sub>)ct],
\n<\/span>which would be orthogonal to a corresponding standing wave function.
\n<\/span>In \u03a8rot<\/sub> , pg<\/sub> is the same momentum of the graviton when free and traveling at the speed of light, B is the internal magnetic field of the electron that is perpendicular to a plane that passes through the center of the electron and is perpendicular to its spin axis, and \u03b1 is the fine-structure constant.\u00a0 Once released again however, the free graviton likely has no rotational component.\u00a0 In fact, it must not if a graviton is to be absorbed by an electron in either of two spin orientations.
\n<\/span>The imaginary component of the complex wave function of an absorbed graviton will be large enough so that it takes several gravitons to make a full charge.\u00a0 Additionally, not all the graviton energy will go into charge contribution; some will contribute to the mass of the electron.
\n<\/span>Not including spin energy, the equation E2<\/sup> = p2<\/sup>c2<\/sup> + (mc2<\/sup>)2<\/sup> represents the relationship between total energy of a particle, the electron in this case, and its linear momentum and rest mass.\u00a0 It is fortunate that the numerical value of pg<\/sub>2<\/sup>\/e<\/em>2<\/sup> is greater than 1 so that we can be more confident that there is an uptick in both mass and linear momentum for an electron in a quantum atomic orbital when a graviton is absorbed.\u00a0 An interesting concept here is that the electron gains linear momentum in the opposite direction, within a certain conical angle, that the free graviton was traveling.
\n<\/span>The rotational energy of an electron was estimated in my April 2007 paper as being 3.06 x 10-9<\/sup> J, and elsewhere on this blog the number of gravitons in an electron was roughly estimated as 3.06 x 10-9<\/sup> J \/ 5.011 x 10-11<\/sup> J = 61.\u00a0 Using the reciprocal of the dimensionless fine-structure constant, the average number of gravitons in an electron, in an atomic orbital at the face of the earth, could possibly be 137\/2 = 68.5.
\n<\/span><\/p>\n


\n<\/span>\u00a0Apr 14 2008, Rev. A: Added a subscript \u201cg\u201d to the representation of the momentum of a free graviton after first mention, and also to the wavelength of a graviton.\u00a0 Added the paragraph \u201cNot including \u2026 was traveling.\u201d<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

The wave function of a free graviton can be written in the form E0 sin (kx-\u03c9t) or B0 sin (kx-\u03c9t) where the wave number k = p\/\u045b, and the electric and magnetic field components are in phase with each other. The momentum of a free graviton, which we will now call pg for purposes seen […]<\/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-49","post","type-post","status-publish","format-standard","hentry","category-quantum-mechanics"],"_links":{"self":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/49","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=49"}],"version-history":[{"count":2,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/49\/revisions"}],"predecessor-version":[{"id":1051,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/49\/revisions\/1051"}],"wp:attachment":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/media?parent=49"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/categories?post=49"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/tags?post=49"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}