The ratio of a circles parameters, circumference or perimeter divided by the diameter, and the very existence of the idea and logic of the largest volume contained by the smallest surface, lends somewhat to divine origin because of Pi's relationship to the building blocks of matter ,the six quark energies. The very act of converting a set of six independent quark masses to a divine origin, the idea of the circle or Pi , is an allowance only made because of the mathematical action caused by the harmonic mean ( or equal treatment ) of the quark energies/masses. The sum of the quark inverse masses equals the logic of the Pi form, largest energy contained by the smallest area, a circle ,disc ,sphere or n-dimensional spheres. In pure translation the harmonic mean of the quark energies is Pi itself, but the angular form is theta or the Golden Ratio...theta = phi = 1.6180339875...as demonstrated below:

Harmonic mean of the quark masses: Pi form ; in proton masses

J.Iuliano

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Physicists have recognized a pattern among these particles, displayed in Table 1.1. The matter particles neatly fall into three groups, which are often called families. Each family contains two of the quarks, an electron or one of its cousins, and one of the neutrino species. The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family. The upshot is that physicists have now probed the structure of matter to scales of about a billionth of a billionth of a meter and shown that everything encountered to date--whether it occurs naturally or is produced artificially with giant atom-smashers--consists of some combination of particles from these three families and their antimatter partners.

A glance at Table 1.1 will no doubt leave you with an even stronger sense of Rabi's bewilderment at the discovery of the muon. The arrangement into families at least gives some semblance of order, but innumerable "whys" leap to the fore. Why are there so many fundamental particles, especially when it seems that the great majority of things in the world around us need only electrons, up-quarks, and down-quarks? Why are there three families? Why not one family or four families or any other number? Why do the particles have a seemingly random spread of masses--why, for instance, does the tau weigh about 3,520 times as much as an electron? Why does the top quark weigh about 40,200 times as much an up-quark? These are such strange, seemingly random numbers. Did they occur by chance, by some divine choice, or is there a comprehensible scientific explanation for these fundamental features of our universe?

Family 1                                    Family 2                         Family 3

Table 1.1 The three families of fundamental particles and their masses (in multiples of the proton mass).The values of the neutrino masses have so far eluded experimental determination.  Particle    Mass    Particle    Mass    Particle    Mass   Electron .00054 Muon .11 Tau 1.9 Electron- neutrino < [10.sup.-8] Muon- neutrino < .0003 Tau- neutrino < .033 Up-quark .0047 Charm Quark 1.6 Top Quark 189  Down-quark   .0074  Strange Quark   .16  Bottom Quark   5.2

The Relative Masses of the
Fundamental Quantum Particles

As Brian Greene pointed out in his book "The Elegant Universe", one of the unsolved mysteries of modern particle physics is why every fundamental particle encountered to date can be group into three families.

"Physicists have recognized a pattern among these particles displayed in the following table. The matter particles neatly fall into three groups, which are often called families. Each family contains two of the quarks an electron or one of its cousins and one of their neutrino species. The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family."

Family 1                                   Family 2                              Family 3

Particle    Mass    Particle    Mass    Particle    Mass   Electron .00054 Muon .11 Tau 1.9 Electron- neutrino  < 10^-8   Muon- neutrino  < .0003   Tau- neutrino < .033 Up-quark .0047 Charm Quark 1.6 Top Quark 189  Down-quark   .0074  Strange Quark   .16  Bottom Quark   5.2

The answer to Brian Greene's question regarding why the particles in the above table have “identical properties except for their mass, which grows larger in each successive family” is related to the resonant "structures" that defined a fundamental quantum particle in Chapter two, the energy vortexes in the continuous non-quantized mass and energy components of space that defines the polarity of the unit electric charge, and the mechanism defining mass derived in Chapters twelve.

                                                       J. Iuliano