finsler geometry, hypercomplex numbers and physics
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"HyperComplex Numbers in Geometry and Physics" 1 (3), vol. 2, 2005
j003

Content of Issue is in the theme. The journal in one file is below.

The notions of distance and velocity modulus in the linear Finsler spaces
2005jaz | Garas'ko G. I., Pavlov D. G.

The formulas for the 3-dimensional distance and the velocity modulus in the 4-dimensional linear space with the Berwald-Moor metrics are obtained. The used algorithm is applicable both for the Minkowski space and for the arbitrary poly-linear Finsler space in which the time-like component could be chosen. The constructed here modulus of the 3-dimensional velocity in the space with the Berwald-Moor metrics coincides with the corresponding expression in the Galilean space at small (non-relativistic) velocities, while at maximal velocities, i.e. for the world lines lying on the surface of the cone of future, this modulus is equal to unity. To construct the 3-dimensional distance, the notion of the surface of the relative simultaneity is used which is analogous to the corresponding speculations in special relativity. The formulas for the velocity transformation when one pass from one inertial frame to another are obtained. In case when both velocities are directed along one of the three selected straight lines, the obtained relations coincide with the analogous relations of special relativity, but they differ in other cases. Besides, the expressions for the transformations that play the same role as Lorentz transformations in the Minkowski space are obtained. It was found that if the three space coordinate axis are straight lines along which the velocities are added as in special relativity, then taking the velocity of the new inertial frame collinear to the one of these coordinate axis, one can see that the transformation of this coordinate and time coordinate coincide with Lorentz transformations, while the transformations of the two transversal coordinates differ from the corresponding Lorentz transformations.


English: Russian:
03-01-e.pdf, 418,171 Kb, PDF 03-01.pdf, 692,959 Kb, PDF


2005jay


English: Russian:
03-02.pdf, 462,948 Kb, PDF


2005jax


English: Russian:
03-03.pdf, 709,1013 Kb, PDF


2005jaw


English: Russian:
03-04.pdf, 490,772 Kb, PDF


2005jav


English: Russian:
03-05.pdf, 540,439 Kb, PDF


2005jau


English: Russian:
03-06.pdf, 586,152 Kb, PDF


2005jat


English: Russian:
03-07.pdf, 506,540 Kb, PDF


2005jas


English: Russian:
03-08.pdf, 823,650 Kb, PDF

Supplement


1992ego


English: Russian:
9207089.pdf, 249,13 Kb, PDF 03-09.pdf, 748,782 Kb, PDF

Journal in one file :


English: Russian:
main-03.pdf, 1865,570 Kb, PDF

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