finsler geometry, hypercomplex numbers and physics
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Hyperbolical analog of the electromagnetic field
2010jaw | Pavlov D.G.  // Research Institute of Hypercomplex Systems in Geometry and Physics, Friazino, Russia, geom2004@mail.ru

On the basis of the analogy of complex numbers analytical functions with two-dimensional electro- and magnetostatic fields there was made an assumption considering the existence of such correspondence between h-analytical functions of the binary variable and some other pair of binary physical fields in reality, one of which is hyperbolical source field and another is hyperbolically vortex field. Unlike electro- and magnetostatic fields, this pair is not realized in space but rather in space-time; thus, the sources of the first field are events while force lines of the second vortex constituent are hyperbolas. Essential feature of this hypothetical pair of fields is that it is feasible only in two-dimensional pseudo-Euclidian space and that it is fundamentally incompatible with the Minkowski idea of 4-dimensional space-time. Partially this is the very reason why such fields weren't considered potentially feasible by physicians even in theory. Their immediate discovery is hampered by experimentalists' being used to space-boundary conditions, while they had better work with space-time ones here. Although this pair is incompatible with Minkowskyi space, still it can possibly be realized in 4-dimesional space possessing, in particular, Berwald-Moor Finsler metric function, its discovery in reality, thus, serving a valid reason to substitute the quadratic metric idea of space-time geometry for Finsler one, connected with quartic form.


English: Russian:
01_pavlov.pdf, 378,28 Kb, PDF

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