Elementary Particles. The Surprising Relationships of Their Masses. A Model and Formulas for Calculating It

A significant number of numerical coincidences were discovered among the masses of all elementary particles and their ratios.The mechanism of figure formation due to the close packing of identical elements with a minimum surface area is examined. This is the packing of soap foam and cells in nature. It occurs in accordance with Plateau's laws. In this case, each element is transformed into a polyhedron. Close packing is characterized by many pentagonal faces, few hexagonal faces, and a minimum of quadrangular faces. A shell of 12 elements fits perfectly on the surface of the first element. After this, the central element transforms into a dodecahedron—a polyhedron whose surface is 12 pentagons. This is the most advantageous polyhedron. Figure 13 appears. 32 elements of the new shell fit into the holes on its surface. Figure 45 appears. The 12 elements of the first shell transform into dodecahedrons. In the same way, adding new shells, we obtain figures 137 and 259, and the last one—421. The especially strong figure 61 is obtained when the second shell contains 16 elements. A fourth shell does not fit on this figure. All these round figures combine into larger ones according to the same rules. Thus, 45 figures of 45 combine into figure 45*45. And 13 figures of 137 produce figure 13*137, and so on. From these round figures, even larger ones emerge, for example, 13*45*137. If the number of elements in such figures and their combinations is divided by four, the mass of the elementary particles (in MeV) is obtained quite accurately. For example: 421 is a muon, its mass is 105.66; 421+137 is a charged pion, its mass is 139.57; 2*45*45 is the ϕ meson; 2*45*137 is the charm meson; 2*137*137 is the beauty meson; 45*137+137*137 is the charm-beauty meson; 4*13*45*137 is the W boson; 4*45*45*45 is the Z boson; 2*45*45*45+4*13*45*137 is the Higgs boson; 61*61 – proton; 61*61+137*137 – beauty baryon;1 – electron (half its mass is the mass of its electric field). Maxwell derived his equations by describing a mechanical model. In it, space is densely filled with large and small round gears that transmit rotation to each other, creating a magnetic field. One might imagine space as being like soap foam, in which the aforementioned gear-shaped figures occupy the entire space. Dirac proposed that space is filled with particles. As long as they lie in a densely packed space, they are invisible and massless. But if a particle is dislodged, a particle and its hole – an antiparticle – appear, expanding space. This is how defects in crystals arise. Particles repel each other, and particles and antiparticles attract. Let's combine the ideas of Maxwell, Dirac, and Plateau's laws. We obtain a space from which various figures can be dislodged. They will create strong positive electrical field. But they can be completely shielded by holes of the same volume. If different shapes and holes combine, they cannot annihilate. For example, the equation for the muon: 421 + 1 = 259 + 137 + 2 * 13 shows that the electric field of the gear “421” can be almost completely shielded by four holes of smaller gears. The difference of 1 is the electric charge of this combined defect. And its mass is the volume of all the gears and holes. And now the formula for the charmed quark, its charge is 2: 45 * 137 + 2 * 13 + 2 = 13 * 421 + 13 * 45 + 3 * 45. This "quark" and its "antiquark," by shielding each other, form a charmed meson.And this is the "quark" of the Z boson: 2 * 45 * 45 * 45 + 137 + 2 = 421 * 421 + 13 * 259 + 13 * 137. The volumes of gears are extremely inconvenient for mutual compensation. Compact combinations are very few. Elementary particles are precisely such combinations. Moreover, in all elementary particles, 13 * 137 is strange; 45 * 137 is charm; 137 * 137 is beauty; 61 * 61 is a baryon.