On a Simpler, Much More General and Truly Marvellous Proof of Fermat’s Last Theorem (I)

Nyambuya, Golden Gadzirayi

doi:10.4236/apm.2016.61001

Cited by 2 publications

(1 citation statement)

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“…Fermat was the first to provide a proof that there is no solution for the case n = 4 (see [16] and also [17]). It has been proved recently that x y z + = has solution, a result which is referred to as the Fermat's Last Theorem for order 2.…”

Section: The Fermat's Last Theorem and Space Time Metricmentioning

confidence: 99%

Origin of Magnetic Fields of Stellar Objects in the Universe Based on the 5D Projection Theory

Fung¹,

Wong²

2017

JMP

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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 3 1 ⊗ D D 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 [4]). We have demonstrated, using the Fermat's Last Theorem [5], that for validity of gauge invariance at the 4D-5D boundary, the 4 th 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 magnetic 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 fi...

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Section: The Fermat's Last Theorem and Space Time Metricmentioning

confidence: 99%