Determinacy

All Fermion Masses Are Determined By Two Constants

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• published: 21 Jul 2016
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All the fermion masses may be determined from merely two numbers dependent on pi , e , and a few rational fractions, and all the fermion charges thereafter. In this, now, dimension independent revision; the electron mass and the ratio of the muon mass to the electron mass are shown calculable from simple quadratic functions of pi , e , and a few rational fractions. All the remaining masses may be determined from from these constants and their indexes determined by the mass-generalized Maxwell’s equations. These calculated masses are all well within current specs as of this publication. In fact, more recent neutrino measurements and estimates have put their values into a rather tight range which the computed values in this update fall within. My book, "Reality is a Mathematical Model" (reference [1]), lays out the foundations of the algebraic construction of the vector-geometry of space-time and how the smooth functions represent the fundamental objects therein. From there, my book, "A Mathematical Preon Foundation for the Standard Model"(reference [2]), gives an introductory look at how fundamental object mass originates from charge; an architecture of these fundamental objects; and the interactions of these fundamental objects. Here, the picture of the mass of the fundamental objects is extended. the mass-generalized Maxwell’s or Maxwell-Cassano equations, are a representation of the equations also obtained from the Helmholtzian matrix product form noted at the begining of my video, [3]: from [2], the fermion architecture is as shown The fermion measured to the greatest accuracy is the electron. It’s current measured value is: m_e ≈ .0.510998928(11) MeV/c^2 However, consider: 1/10{15/8 + 1/4000 * (486/25)}e = 0.5109989278047020776144390005897 Since this is right in the middle of the margin of error of a quantity measured to eight significant figures, it is not even remotely out of line to make the assignment: m_e = 1/10{15/8 + 1/4000 * (486/25)}e The mass of the electron as the basis. The mass relationships simplify as shown From these tables the constant k may be determined, as well as a host of relationships between the fermion masses. The upper generation fermion masses fill out the following table. (It is rather remarkable how simple the relationships are.) as this table shows: the constant k may be established as shown, here, dependent on pi , 15/8 & 1/4000 (just as the electron mass is). k = 4*pi^2 + 15/8 +(1/4000)(20/21) So, all the fermion masses may be computed from the above formulas and tabulated as follows, along side reported massvalues. There are variations between the references on some of the masses, but the tightest ranges have been used, and the value centered in the error range. All the calculated masses above are accurate well within their margin of error. The error ranges for all the masses are rather tight (even the neutrino mass estimates, now), so confidence on the formulation is high. There is an affine transformation that relates the above two constants to two rational fractions: m(3,1)/(e/10) / 1 Mev/c^2 = (15/8) + (486/25)*(1/4000) k = (15/8) + (20/21)*(1/4000) + 4*pi^2 Thus, the masses of all the fermions may be calculated from merely two fixed constants indexed via the field strength components of the mass-generalized Maxwell’s equations. (Maxwell-Cassano equations) References [1] Cassano, Claude.Michael ; "Reality is a Mathematical Model", 2010. ISBN: 1468120921 ; http://www.amazon.com/dp/1468120921 ASIN: B0049P1P4C ; http://www.amazon.com/Reality-Mathematical-Model-ebook/dp/B0049P1P4C/ref= tmm_kin_swatch_0?_encoding=UTF8&sr;=&qid;= [2] Cassano, Claude.Michael ; "A Mathematical Preon Foundation for the Standard Model", 2011. ISBN:1468117734 ; http://www.amazon.com/dp/1468117734 Cassano, Claude.Michael ; "The Standard Model Architecture and Interactions 1" ; http://www.youtube.com/watch?v=GFlmF6WWGxE Cassano, Claude.Michael ; "The Standard Model Architecture and Interactions Part 1" ; http://www.dnatube.com/video/6907/The-Standard-Model-Architecture-and-Interactions-Part-1 http://www.scivee.tv/node/28362 Cassano, Claude.Michael ; "The Standard Model Architecture and Interactions Part 2" ; http://www.youtube.com/watch?v=Mxa2u7-czmk Cassano, Claude.Michael ; "The Standard Model Architecture and Interactions Part 2" ; http://www.dnatube.com/video/6908/The-Standard-Model-Architecture-and-Interactions-Part-2 http://www.scivee.tv/node/28373 [3] Cassano, Claude.Michael ; "A Helmholtzian operator and electromagnetic-nuclear field" ; http://www.dnatube.com/video/6877/A-Helmholtzian-operator-and-electromagnetic-nuclear-field