Relativistic Stereometric Coordinates from Relativistic Localizing Systems and the Projective Geometry of the Spacetime Manifold

Abstract : Relativistic stereometric coordinates supplied by relativistic auto-locating positioning systems made up of four satellites supplemented by a fifth one are defined in addition to the well-known emission and reception coordinates. Such a constellation of five satellites defines a so-called relativistic localizing system. The determination of such systems is motivated by the need to not only locate (within a grid) users utilizing receivers but, more generally, to localize any spacetime event. The angles measured on the celestial spheres of the five satellites enter into the definition. Therefore, there are, up to scalings, intrinsic physical coordinates related to the underlying conformal structure of spacetime. Moreover, they indicate that spacetime must be endowed everywhere with a local projective geometry characteristic of a so-called generalized Cartan space locally modeled on four-dimensional, real projective space. The particular process of localization providing the relativistic stereometric coordinates is based, in a way, on an enhanced notion of parallax in space and time generalizing the usual parallax restricted to space only.
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Pré-publication, Document de travail
The paper has been accepted for publication with a slighly different title : "Relativistic Pentam.. 2014
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https://hal.inria.fr/hal-01025947
Contributeur : Jacques Rubin <>
Soumis le : mardi 22 juillet 2014 - 17:39:28
Dernière modification le : jeudi 3 mai 2018 - 13:08:04
Document(s) archivé(s) le : mardi 11 avril 2017 - 16:10:13

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  • HAL Id : hal-01025947, version 2
  • ARXIV : 1407.5157

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Jacques Rubin. Relativistic Stereometric Coordinates from Relativistic Localizing Systems and the Projective Geometry of the Spacetime Manifold. The paper has been accepted for publication with a slighly different title : "Relativistic Pentam.. 2014. 〈hal-01025947v2〉

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