{"id":212,"date":"2010-04-09T06:40:30","date_gmt":"2010-04-09T11:40:30","guid":{"rendered":"http:\/\/www.fruechtetheory.com\/blog\/?p=212"},"modified":"2010-04-09T06:40:30","modified_gmt":"2010-04-09T11:40:30","slug":"origin-of-mass","status":"publish","type":"post","link":"https:\/\/www.fruechtetheory.com\/blog\/2010\/04\/09\/origin-of-mass\/","title":{"rendered":"Origin of Mass"},"content":{"rendered":"

In the complex number system (a \u2013 bi) is the conjugate of (a + bi).\u00a0 For a wave function, e-ikx<\/sup> is the conjugate of eikx<\/sup>, where:<\/p>\n

eikx<\/sup> = cos kx + i sin kx, and<\/p>\n

e-ikx<\/sup> = cos kx – i sin kx<\/p>\n

Gravitons passing through an electron, proton, or neutron create potential wells for the standing waves inside these particles, which internal waves are in bound states.\u00a0 To borrow from Kronig-Penny Hamiltonian math, in the \u201cwell domain of the potential array\u201d ([1], pg 295) we may have:<\/p>\n

\u03c6I<\/sub> = Ae^ik1<\/sub>x + Be^-ik1<\/sub>x,<\/p>\n

and in the \u201cbarrier domain\u201d:<\/p>\n

\u03c6II<\/sub> = Ce^ik2<\/sub>x + De^-ik2<\/sub>x,\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0([1], (8.65), pg 307)<\/p>\n

The speed of a conjugate wave graviton slows to less than the speed of light in a vacuum as it passes through an electron or a nucleus.\u00a0 Its frequency stays the same while its amplitude increases.\u00a0 Coming free out the other side, the graviton resumes the speed of light in a vacuum and returns to lower amplitude.\u00a0 Gravitons arriving isotropically, with the exception of those absorbed and becoming mass, help cradle the particle mass and, in summation, gravitational pressure at the boundary between the well and barrier domains holds particle mass together and keeps it from flying apart.<\/p>\n

The letter k is used for wave number, which is in units of radians per meter.\u00a0 Since k1<\/sub> > k2<\/sub>, the full wavelength is shorter in distance for \u03c6I<\/sub> compared to \u03c6II<\/sub>, the conjugate wave graviton then being compacted within a subatomic particle.\u00a0 The conjugate graviton would also have a rotational component in phase with a corresponding rotational component constituent to the mass and earlier written [2], in the well domain.<\/p>\n

In terms of a Fourier transform of dimension inside the particle mass we have:<\/p>\n

d(x-x0<\/sub>) \u00a0= \u00a0(1\/(2\u03c0\u045b)) \u222b-\u00a5<\/sub>+\u00a5<\/sup> dp eip(x-x<\/sup>0<\/sup>)\/\u045b<\/sup>\u00a0 =\u00a0 (1\/(2\u03c0)) \u222b-\u00a5<\/sub>+\u00a5<\/sup> dk eik(x-x<\/sup>0<\/sup>)<\/sup> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0([3], (34), pg 1473)<\/p>\n

where x0<\/sub> is the position of the particle, k is k1<\/sub> from above, and p is the momentum of a graviton otherwise known as pg<\/sub> [2].<\/p>\n

As some gravitons escape into deep space, entropy in the universe is always increasing from a state of original creation, \u2013 no \u201cbig bang\u201d.\u00a0 The force we have all been aware of our entire lives may be associated with the single source of all energy and mass.<\/p>\n

\u00a0<\/p>\n

[1] Liboff, Richard L., Introductory Quantum Mechanics, Fourth Edition<\/span>, Addison Wesley, 2003<\/p>\n

[2] https:\/\/www.fruechtetheory.com\/blog\/2008\/04\/01\/wave-function-transfer-2-2\/<\/a><\/p>\n

[3] Cohen-Tannoudji, Dui, Lalo\u00eb, Quantum Mechanics<\/span>, Hermann, 1977, Paris, France, Appendix II<\/p>\n

\u00a0<\/p>\n

PS: The Dirac delta symbol and plus and minus infinity limits of integration in the Cohen-Tannoudji, Dui, Lalo\u00eb equation do not transfer into this blog properly.\u00a0 Go to reference [3] if you want more clarity.<\/p>\n","protected":false},"excerpt":{"rendered":"

In the complex number system (a \u2013 bi) is the conjugate of (a + bi).\u00a0 For a wave function, e-ikx is the conjugate of eikx, where: eikx = cos kx + i sin kx, and e-ikx = cos kx – i sin kx Gravitons passing through an electron, proton, or neutron create potential wells for […]<\/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-212","post","type-post","status-publish","format-standard","hentry","category-quantum-mechanics"],"_links":{"self":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/212","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=212"}],"version-history":[{"count":1,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/212\/revisions"}],"predecessor-version":[{"id":213,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/212\/revisions\/213"}],"wp:attachment":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/media?parent=212"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/categories?post=212"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/tags?post=212"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}