摘要
The least massive fermion generation is attributed to an analogue of Weyl curvature which occurs when a closed, spin-string sweeps out a closed world tube: , where S represents string length. A second order tube and consequent second order fermion mass are associated with a closed tube which circulates and itself sweeps out a closed tube: . Finally a Kth order tube and kth order fermion generation are associated with the general expression . By hypothesis six world tube orders establish an SU(3) symmetry and each closed tube interacts with a SUGRA connection of spin-. Such connections can either be photon-fermion composites or composites that consist strictly of fermions. Interactions that involve no photons are, by hypothesis unobserved and are therefore associated with closed world tubes that are classified as dark mass-energy. It is demonstrated that interactions involving ordinary mass-energy are identities (e.g. interactions that are incapable of generating the proposed SU(3) symmetry). It is therefore concluded that dark mass-energy is a necessary condition for the SU(3) symmetry that by hypothesis characterizes the proposed model. Since 95% of the mass-energy in the universe is regarded as dark, the total mass-energy that constitutes the proposed SU(3) symmetry can be calculated as , where QL is a left-handed quark, where ΨL is a left-handed spin particle and where is a right-handed anti-lepton. Thus the mass-energy that is associated with the wave is about 1067 GeV/c2 (the approximate mass of a typical galaxy). This wave is regarded by hypothesis as a single galactic unit and as the ground state of a large-scale quantization;i.e. as the ground state of a series of abstract waves which mimic de Broglie waves in the sense that the ground state is a wave of one anti-node which oscillates about a wave length that parallels a geodesic on a smallest abstract spherical shell. The first excited state is a wave of two anti-nodes that oscillate about a wave length that parallels a geodesic on the second smallest spherical shell etc. The proposed quantization is calibrated by a boundary condition which is established by observation and which separates galaxies by distances that are about ten times the diameter of a typical galaxy;separates clusters by distances that are about ten times the diameter of a typical cluster etc. Thus the wave Φis, by hypothesis, the first in a series of gauge transformations that models the galactic hierarchy. By hypothesis the above gauge transformations form an irre-ducible representation of the SU(3) symmetric hierarchy of fermionic generations that is introduced above, providing that tensor products are replaced by the six increments which correspond to the proposed gauge transformations. By hypothesis the local cluster (the state corresponding to n = 2) results from the dispersion of those galaxies that originally form the 2-spherical area by which the local cluster is bounded. This number of galaxies is said to be at least 54. Thus the radius of the concentric sphere which forms the original 2-dimensional boundary of the local cluster is approximately mean radial units. Accordingly the area of the concentric sphere that corresponds to n = 6 is approximately ?galactic units;or if one predicts 79 galaxies for the local cluster, then the proposed model indicates a universe of approximately 2 × (1012) galaxies, as established by the C. Conselice team at the University of Nottingham and by NASA.
The least massive fermion generation is attributed to an analogue of Weyl curvature which occurs when a closed, spin-string sweeps out a closed world tube: , where S represents string length. A second order tube and consequent second order fermion mass are associated with a closed tube which circulates and itself sweeps out a closed tube: . Finally a Kth order tube and kth order fermion generation are associated with the general expression . By hypothesis six world tube orders establish an SU(3) symmetry and each closed tube interacts with a SUGRA connection of spin-. Such connections can either be photon-fermion composites or composites that consist strictly of fermions. Interactions that involve no photons are, by hypothesis unobserved and are therefore associated with closed world tubes that are classified as dark mass-energy. It is demonstrated that interactions involving ordinary mass-energy are identities (e.g. interactions that are incapable of generating the proposed SU(3) symmetry). It is therefore concluded that dark mass-energy is a necessary condition for the SU(3) symmetry that by hypothesis characterizes the proposed model. Since 95% of the mass-energy in the universe is regarded as dark, the total mass-energy that constitutes the proposed SU(3) symmetry can be calculated as , where QL is a left-handed quark, where ΨL is a left-handed spin particle and where is a right-handed anti-lepton. Thus the mass-energy that is associated with the wave is about 1067 GeV/c2 (the approximate mass of a typical galaxy). This wave is regarded by hypothesis as a single galactic unit and as the ground state of a large-scale quantization;i.e. as the ground state of a series of abstract waves which mimic de Broglie waves in the sense that the ground state is a wave of one anti-node which oscillates about a wave length that parallels a geodesic on a smallest abstract spherical shell. The first excited state is a wave of two anti-nodes that oscillate about a wave length that parallels a geodesic on the second smallest spherical shell etc. The proposed quantization is calibrated by a boundary condition which is established by observation and which separates galaxies by distances that are about ten times the diameter of a typical galaxy;separates clusters by distances that are about ten times the diameter of a typical cluster etc. Thus the wave Φis, by hypothesis, the first in a series of gauge transformations that models the galactic hierarchy. By hypothesis the above gauge transformations form an irre-ducible representation of the SU(3) symmetric hierarchy of fermionic generations that is introduced above, providing that tensor products are replaced by the six increments which correspond to the proposed gauge transformations. By hypothesis the local cluster (the state corresponding to n = 2) results from the dispersion of those galaxies that originally form the 2-spherical area by which the local cluster is bounded. This number of galaxies is said to be at least 54. Thus the radius of the concentric sphere which forms the original 2-dimensional boundary of the local cluster is approximately mean radial units. Accordingly the area of the concentric sphere that corresponds to n = 6 is approximately ?galactic units;or if one predicts 79 galaxies for the local cluster, then the proposed model indicates a universe of approximately 2 × (1012) galaxies, as established by the C. Conselice team at the University of Nottingham and by NASA.
