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Identifying the four I-frame quarks is done through logical deduction, based on the hypothesis that the energy of individual T and V particles are exactly the same. Piotr Zenczykowski <a href="http://arxiv.org/abs/0803.0223">outlines an O(6) phase space</a> using Clifford Algebras. We surmise that:
... yet as only "T" (electrical charge) can interact with T particles, the additional mass of the V particles being dragged around results in an incorrect inference that the larger compound particles have a higher mass. The most immediate example of these is the neutron and the proton. A neutron is not susceptible to movement by electrical charge. It would therefore be reasonable (but logically incorrect) to assume that, because it cannot be moved by an electrical charge it must automatically have an infinite mass! Clearly, however, this is not true: we know instead that its mass is near-identical to that of a proton.
In the Rishon Model, both the neutron and the proton comprise nine T and V particles in total. It is therefore quite reasonable to postulate a hypothesis that the T and V particles are of equal energy. However, what possible reasonable mathematical deductions could be put forward which support this hypothesis? Surmising that the deductive process for calculating the mass of elementary particles from their trails in particle physics chambers under the influence of electrical fields is based on cubic and square laws, the ratios of masses of various particles was put through a cube-root and square-root wringer. By a process of trial and error, some clear patterns emerged. The following figures for mass for various particles were used:
Starting with the lower-energy particles (and using python as a calculator) we take the first example.
electron and the up quark:
So the 2/3s root of the mass ratios of the up quark and the electron is very close to 5/2 (within 0.658%)
Note: the mass of the electron itself can be expressed in terms of the speed of light, planck's constant and simple integers. The figure given is accurate to six decimal places
electron to down quark:
So the 2/3s root of the mass ratios of the up quark and the electron is very close to 4*10/9 (within 0.029%)
Note: also of note is that the cubic root of the mass ratio of the up quark and the electron is close to (11 * e) / (7 * 9), to within 0.073%. The exact significance of this is not known.
up quark to down quark:
So the cubic-root of the mass ratios of the up quark and down quark is very close to 4/3 (within 0.18%)
muon and the electron:
»> x = 0.105658 / 0.000511 »> x 206.767 »> pow(x, 0.666666667) 34.96667 »> pow(x, 0.666666667) / 35 0.999048
So the 2/3s root of the mass ratios of the muon and the electron is very close to 35/1 (within 0.095%).
Note also the following interesting observation:
>>> pow(x, 0.5) / golden_mean_ratio * 9
79.983
So the square root of the mass ratios of the muon and the electron is 80 * golden mean ratio, divided by 9 (to 4 decimal places).
proton and the electron:
>>> import math
>>> c = 2.99792458e8
>>> bmr_proton = 0.00152103220215
>>> x = 938.272/.510998
>>> starpiproton = (1 + (math.pi * bmr_proton /1.057))
>>> print "star pi bmr_proton", starpiproton
>>> starpiproton = 1+1/pow(math.pi*7.7/4, 3)
>>> print "star pi bmr_proton", starpiproton
>>> print x / pow(c, 0.333333333333) / math.pi / math.pi * 4 * 9 / 10
>>> print x / pow(c/math.pi, 0.333333333333) / 4 / starpiproton
1.00000037067
So, to six decimal places, the ratio of the mass of the proton and the mass of the electron can be expressed purely in terms of pi, the speed of light, a few cubic expressions, some small integers and the number 7.7 (which is 8.0 - 0.3).
tau and the muon:
»> x = 1.7768 / 0.105658 »> x 16.817 »> pow(x, 0.666666667) 6.5338 »> pow(x, 0.666666667) * 8 52.5
So the 2/3s root of the mass ratios of the tau and the muon is very close to 16/105 (within 0.020%). Note also that the square root of the tau to muon ratio is almost exactly 4.1 (within 0.019%)
proton and the muon:
»> x = 0.938 / 0.105658 »> x 8.877699 »> pow(x, 0.666666667) 4.28746 »> pow(x, 0.666666667) * 7 30.01223
So the 2/3s root of the mass ratios of the muon and the proton is very close to 7/30 (within 0.041%). Note also that the square root of the proton to muon ratio is very close to 3 (within 0.68%)
proton and the tau:
»> x = 1.7768 / 0.938 »> x 1.8942 »> pow(x, 0.666666667) 1.5309 »> pow(x, 0.666666667) * 32 48.99033
So the 2/3s root of the mass ratios of the tau and the proton is very close to 7*7/32 (within 0.020%). Note also that the square root of the proton to muon ratio is very close to 11/8 (within 0.096%)
proton and the charm quark:
»> x = 1.29 / 0.938 »> x 1.375 »> pow(x, 0.666666667) 1.237 »> pow(x, 0.666666667) * 4 4.947
So the 2/3s root of the mass ratios of the charm quark and proton is very close to 5/4 (within 1.06%)
Bottom and charm quark (upper, larger measured mass figure for bottom):
»> x = 4.65 / 1.29 »> x 3.605 »> pow(x, 0.666666667) 2.351 »> pow(x, 0.666666667) * 3 7.0528
2/3 root mass-ratio bottom (larger estimate) to charm: 7/3
Bottom and charm quark (lower, smaller measured mass figure for bottom):
»> x = 4.18 / 1.29 »> x 3.240 »> pow(x, 0.333333333) 1.480 »> pow(x, 0.333333333) * 2 2.960
cubic root mass-ratio bottom (lower estimate) to charm: 3/2 (within 1.35%)
»> x = 4.18 / 1.29 »> x 3.240 »> pow(x, 0.5) 1.800086 »> pow(x, 0.5) * 5 9.00043
square root mass-ratio bottom (lower estimate) to charm: 9/5 (within 0.0048%)
Bottom and proton (lower, smaller measured mass figure for bottom):
»> x = 4.18 / 0.938 »> x 4.456 »> pow(x, 0.5) 2.11099 »> pow(x, 0.5) * 9 / 19 0.999943
square root mass-ratio bottom (lower estimate) to proton: 19/9 (within 0.0056%)
top and bottom (lower mass figure for bottom):
»> x = 173.07 / 4.18 »> x 41.404 »> pow(x, 0.666666667) 11.968
2/3s root mass-ratio top to bottom (lower estimate): 12 to 1 (within 0.26%)
»> x = 173.07 / 4.18 »> x 41.404 »> pow(x, 0.5) 6.435 »> pow(x, 0.5)*7/45. 1.00094
square root mass-ratio top to bottom (lower estimate): 7 to 45 (within 0.094%)
also noteworthy is that the cube-root of the two same mass ratios is (e * 11 / 14) to within five decimal places (0.0034%).
strange to charm:
»> x = 1.29 / 0.090 »> x 14.333 »> pow(x, 0.3333333) 2.429 »> pow(x, 0.3333333)*7 17.004
cubic root mass-ratio of charm to strange: 17/7 (within 0.022%)
also noteworthy is that the cube-root of the two same mass ratios is (e * 5) / (3 * 11) to within four decimal places (0.046%).
higgs to top:
»> x = 173.07 / 126 »> x 1.37357 »> pow(x, 0.3333333) 1.112 »> pow(x, 0.3333333)*9 10.0044
cubic root mass-ratio of top to higgs: 10/9 (within 0.044%) Note: the exact significance of this ratio is unclear as the composition of the Higg's Boson in terms of Rishon particles has yet to be analysed.
mass of proton to sum of mass of its quarks:
»> 0.00479 * 2 + 0.00201 0.01159 »> x = 0.938 / 0.01159 »> x 80.932 »> pow(x, 0.3333333) 4.326 »> pow(x, 0.3333333)*3 12.977
cubic root mass-ratio of proton to sum of its quark mass: 13/3 (within 0.18%) Note: the exact significance of this ratio is unclear.