# Golden Section

56 57 aPPenDix iv Designers recTangles aPPenDix v golDen Physics From Hambidge. Key ws whirling square golden rectangle, s square, v5 root 5 rectangle David Bohm s deep platonic insights into nature s superimplicate, implicate explicate orders may be combined with M.S. El Naschie s Einfinity E theory. This models a harmonic production of quarks and elementary particles through a golden section centred Cantorian spacetime. Bohm maintained that there is an inner, hidden implicate order analogous to Plato s intelligible realm lying behind the outer explicate order Plato s sensible realm. He argued that this source of order and structure was discoverable in the so called vacuum state, the zeropoint energy field. In seminars at Birkbeck he asserted In one cubic centimeter of socalled empty space, the amount of energy is much greater than the total energy of all the matter in the known universe Matter is merely an excitation on the virtual sea of the implicate order. Reminiscent of Plato s prisoner watching the shadows on the cave wall, Bohm maintained that the fractal discontinuity or sudden jumps at the quantum level may be considered as a shadow crossing the wall . M.S. El Naschie s contribution provides the detailed content for Bohm s platonic conceptual framework. Beginning with his 1994 paper, Is Quantum Space a Random Cantor Set with a Golden Mean Dimension at the Core the E spacetime theory provides a profound theoretical basis for the central role the golden section plays as the winding number in the harmonic manifestation of quark and subatomic particle masses through the continuous symmetry breaking of vacuum state fluctuations The appearance of the Golden Mean, its inverse as well as its square value with both negative and positive signs as the frequency of vibration and massenergy factor indicate that it is the simplest realistic unit from which a Hamiltonian dynamics can start developing a highly complex structure, a so called nested vibration . The Golden Mean plays a decisive role in nonlinear dynamical stability and chaotic systems as shown in the celebrated KAM theorem Chaos Border of Kolmogorov, Arnold and Moser and in high energy particle physics . The KAM theorem asserts that the most stable periodic orbit is that which has an irrational ratio of resonance frequencies. Since the Golden Mean is the most irrational number the corresponding orbit is the most stable orbit . In the view of string theory, particles are vibrating strings. Therefore to observe a particle, the corresponding vibration must be stable and that is only possible in the KAM interpretation which we call the VAK Cantorian theory of vacuum fluctuation, when the winding number corresponding to this dynamics is equal to the Golden Mean. El Naschie El Naschie discovered that particle physics seen through the eyes of E appears to be a cosmic symphony. The particles are a rather noncomplex function of the golden mean and its derivatives. The following E quark masses are in excellent agreement with the majority of the scarce and difficult to obtain data about the mass of quarks. It takes only one look at these values for anyone to realise that they form a harmonic musical ladder. Current Constituent Quark Mass as Functions of F and 1F. Quark Flavor Current Mass MeV Constituent Mass MeV Up 2 F 2 5.236 80 F 3 338.885 Down 2 F 3 8.472 80 F 3 338.885 Strange 10 F 6 179.442 10 F 8 469.787 Charm 300 F 3 1,270.82 20 F 9 1,520.263 Beauty Bottom 10 3 F 3 4,236.067 100 F 8 4,697.871 Truth Top 10 4 F 3 42,360.679 10 4 F 6 179,442.719 In the table below, notice the close agreement between the theoretical and the experimental values, and the interesting presence of the 52 phyllotaxis and Lucas 74 ratios. The E values of the fundamental constituents involved below are as follows a0 20 F4 137.0820 is the inverse Sommerfield electromagnetic fine structure coupling constant. F31 F3 0.12033988 is a Fbased constant. ag 10 F3 42.3606797 is the theoretical value of the coupling constant a0 at the point where three nongravitational forces intersect. ags agF 26.18033988 10 F3 F 10 F2. This is the inverse coupling constant at the super symmetric unification of all fundamental forces taking place at the Planck length of 1033 cm. Subatomic Particle Mass as a Function of F and 1F. subatomic particle e electron n neutron P proton P P meson P0 Exi Exi 0 muon h h theoretical mass MeV ags10 10 F210 0.51166 20 F8 939.574 20 F8 cos p60 938.28 a0 52 139.5820 a0 52 134.5820 10 a0 49F 1,673.657 10 a0 8F 1,321.377 10 a0 9F 1,315.197 1000 F5 105.309 or 20 5 F3 105.665 4 a gs 220 40 F 2220 548.328 mh 74 mh 7804 ags2 959.5742755 experimental value MeV 0.511 939.563 938.27231 139.57 134.98 1,672.43 1,321.32 1,314.9 105.65839 548.8 957.5