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Maarten Tom
de Hoop
QM is
mathematically analyzed in the infinite dimensional complex
Hilbert space. As is known all elementary particles have energy directly proportional to frequency. These particle-own vibrations should appear in the 2D-plane perpendicular to the observed position of the elementary particle as mathematically described on the 1D-worldline. The maximum distance ρ_{max} from the vibrating point compared to the average position on the world-line is now twice the minimum distance ρ_{min} > 0. The average distance from the average worldline now is directly proportional to: <ρ> ÷ Planck length x spin x Golden Ratio . I was happy with this result, because this is exactly why the Golden Ratio is observed so frequently. The solution of the second-order DE, which basically describes the spin (helicity), had the second constant exactly equal to the Golden Ratio (φ = 1 + 1/φ). The solution space of this SR DE also explains why the QM has to be solved in complex Hilbert space. I.e. this solves problem 6 of the math. problems presented in 1900 by David Hilbert. In this mathematical symmetries analysis all elementary particles are completely explained. Mathematically knots are only possible in SR 4D-spacetime. All (elementary) fermions described as extended particles have second-order DE which have to be solved with open BC. Bosons have to be solved with closed BC, so only contain one so-called family for ever possible symmetry group in 4D-spacetime. Open BC have one positive integer as extra degree of freedom, compared to closed BC. This integer specifies the particle family of an elementary fermion. Our universe has 3 different families of fermions. Open BC describe elementary particles (fermions) which interact in all directions and as a result of that simple mathematical fact always interact with the gravitational field, i.e. have non-zero masses. Consequently, in a simple SR description the harmonic oscillating path of a fermion allows reversal of direction. So fermions allow knots in their harmonic oscillating path. Without fermions no sources for force-particles (bosons), so nothing at all. The only possible mathematical analysis of our reality is 4D-spacetime, because only in this space(time) knots are mathematical possible. This simple fact was proven in 2004 by Grigori Perelman. Last change: 16-09-2014 19:11:36 |