Abstract
Beginning with a 5D homogeneous universe [1], we have provided a plausible explanation of the self-rotation phenomenon of stellar objects previously with illustration of large number of star samples [2], via a 5D-4D projection. The origin of such rotation is the balance of the angular momenta of stars and that of positive and negative charged e-trino pairs, within a 3D ⊗ 1D void of the stellar object, the existence of which is based on conservation/parity laws in physics if one starts with homogeneous 5D universe. While the in-phase e-trino pairs are proposed to be responsible for the generation of angular momentum, the anti-phase but oppositely charge pairs necessarily produce currents. In the 5D to 4D projection, one space variable in the 5D manifold was compacted to zero in most other 5D theories (including theories of Kaluza-Klein and Einstein [3] [4]). We have demonstrated, using the Fermat’s Last Theorem [5], that for validity of gauge invariance at the 4D-5D boundary, the 4th space variable in the 5D manifold is mapped into two current rings at both magnetic poles as required by Perelman entropy mapping; these loops are the origin of the dipolar magnetic field. One conclusion we draw is that there is no gravitational singularity, and hence no black holes in the universe, a result strongly supported by the recent discovery of many stars with masses well greater than 100 solar mass [6] [7] [8], without trace of phenomena observed (such as strong gamma and X ray emissions), which are supposed to be associated with black holes. We analyze the properties of such loop currents on the 4D-5D boundary, where Maxwell equations are valid. We derive explicit expressions for the dipolar fields over the whole temperature range. We then compare our prediction with measured surface magnetic fields of many stars. Since there is coupling in distribution between the in-phase and anti-phase pairs of e-trinos, the generated mag-netic field is directly related to the angular momentum, leading to the result that the magnetic field can be expressible in terms of only the mechanical variables (mass M, radius R, rotation period P)of a star, as if Maxwell equations are “hidden”. An explanation for the occurrence of this “un-expected result” is provided in Section (7.6). Therefore we provide satisfactory answers to a number of “mysteries” of magnetism in astrophysics such as the “Magnetic Bode’s Relation/Law” [9] and the experimental finding that B-P graph in the log-log plot is linear. Moreover, we have developed a new method for studying the relations among the data (M, R, P) during stellar evolution. Ten groups of stellar objects, effectively over 2000 samples are used in various parts of the analysis. We also explain the emergence of huge magnetic field in very old stars like White Dwarfs in terms of formation of 2D Semion state on stellar surface and release of magnetic flux as magnetic storms upon changing the 2D state back to 3D structure. Moreover, we provide an explanation, on the ground of the 5D theory, for the detection of extremely weak fields in Venus and Mars and the asymmetric distribution of magnetic field on the Martian surface. We predict the equatorial fields B of the newly discovered Trappist-1 star and the 6 nearest planets. The log B − log P graph for the 6 planets is linear and they satisfy the Magnetic Bode’s relation. Based on the above analysis, we have discovered several new laws of stellar magnetism, which are summarized in Section (7.6).
Highlights
Understanding Our Universe by Expanding the 4D Lorentz Manifold to the 5D Homogeneous Manifold and Project Back to the 4D Space-Time Structure via Two Projection ProceduresIt is a very important step in physics to unify gravity with electrodynamics
The origin of such rotation is the balance of the angular momenta of stars and that of positive and negative charged e-trino pairs, within a 3D ⊗1D void of the stellar object, the existence of which is based on conservation/parity laws in physics if one starts with homogeneous 5D universe
We have demonstrated, using the Fermat’s Last Theorem [5], that for validity of gauge invariance at the 4D-5D boundary, the 4th space variable in the 5D manifold is mapped into two current rings at both magnetic poles as required by Perelman entropy mapping; these loops are the origin of the dipolar magnetic field
Summary
Detail of the 4D Maxwell boundary can be explicitly analyzed through Fermat's theorem, in terms of Abelian angles. It is this explicit split that is revealed as 2 spherical gamma ray bubbles, one above and one below the Center of the Milky Way galactic core observed by NASA [19] By this parity split, the vector potential field solutions of the 5D homogeneous metric equation with 2nd order operator breaks the 5D symmetry in the Maxwell sub-space-time, eliminating the magnetic mono-pole solution. The result is that there is imposition in alignment between r′ of the Fermat's sum in 5D, and r that of the Fermat's sum in 4D This boundary continuity leads to the manifestation of a Ricci Flow direction, which will convert the homogeneous Maxwell 4D boundary through the two projections (Po & P1) of the already broken symmetric property of the 4 space coordinates further into a 4D Lorentz manifold containing masses. The measure of this 1D loop depends on the hadrons created through P1 in the Lorentz mass shell domain
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