dorsal/arxiv
View SchemaThe Euclidean geometry deformations and capacities of their application to microcosm space-time geometry
| Authors | Yuri A. Rylov |
|---|---|
| Categories | |
| ArXiv ID | physics/0206017 |
| URL | https://arxiv.org/abs/physics/0206017 |
Abstract
Usually a Riemannian geometry is considered to be the most general geometry, which could be used as a space-time geometry. In fact, any Riemannian geometry is a result of some deformation of the Euclidean geometry. Class of these Riemannian deformations is restricted by a series of unfounded constraints. Eliminating these constraints, one obtains a more wide class of possible space-time geometries (T-geometries). Any T-geometry is described by the world function completely. T-geometry is a powerful tool for the microcosm investigations due to three its characteristic features: (1) Any geometric object is defined in all T-geometries at once, because its definition does not depend on the form of world function. (2) Language of T-geometry does not use external means of description such as coordinates and curves; it uses only primordially geometrical concepts: subspaces and world function. (3) There is no necessity to construct the complete axiomatics of T-geometry, because it uses deformed Euclidean axiomatics, and one can investigate only interesting geometric relations. Capacities of T-geometries for the microcosm description are discussed in the paper. When the world function is symmetric and T-geometry is nondegenerate, the particle mass is geometrized, and nonrelativistic quantum effects are described as geometric ones, i.e. without a reference to principles of quantum theory. When world function is asymmetric, the future is not geometrically equivalent to the past, and capacities of T-geometry increase multiply. Antisymmetric component of the world function generates some metric fields, whose influence on geometry properties is especially strong in the microcosm.
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"abstract": "Usually a Riemannian geometry is considered to be the most general geometry,\nwhich could be used as a space-time geometry. In fact, any Riemannian geometry\nis a result of some deformation of the Euclidean geometry. Class of these\nRiemannian deformations is restricted by a series of unfounded constraints.\nEliminating these constraints, one obtains a more wide class of possible\nspace-time geometries (T-geometries). Any T-geometry is described by the world\nfunction completely. T-geometry is a powerful tool for the microcosm\ninvestigations due to three its characteristic features: (1) Any geometric\nobject is defined in all T-geometries at once, because its definition does not\ndepend on the form of world function. (2) Language of T-geometry does not use\nexternal means of description such as coordinates and curves; it uses only\nprimordially geometrical concepts: subspaces and world function. (3) There is\nno necessity to construct the complete axiomatics of T-geometry, because it\nuses deformed Euclidean axiomatics, and one can investigate only interesting\ngeometric relations. Capacities of T-geometries for the microcosm description\nare discussed in the paper. When the world function is symmetric and T-geometry\nis nondegenerate, the particle mass is geometrized, and nonrelativistic quantum\neffects are described as geometric ones, i.e. without a reference to principles\nof quantum theory. When world function is asymmetric, the future is not\ngeometrically equivalent to the past, and capacities of T-geometry increase\nmultiply. Antisymmetric component of the world function generates some metric\nfields, whose influence on geometry properties is especially strong in the\nmicrocosm.",
"arxiv_id": "physics/0206017",
"authors": [
"Yuri A. Rylov"
],
"categories": [
"physics.gen-ph"
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"title": "The Euclidean geometry deformations and capacities of their application to microcosm space-time geometry",
"url": "https://arxiv.org/abs/physics/0206017"
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