Communication Dans Un Congrès Année : 2018

Consequences in fields theory and astrophysics of a projective theory of relativity emerging from relativistic localizing systems

Résumé

The existence of a three-dimensional projective geometry in spacetime, in particular in the Minkowski spacetime, was already well-known early from the very beginning of the theory of relativity. This geometry is clearly linked up with well-identified physical observables. On the contrary, no such identifications were found out for higherdimensional projective geometries of spacetime. And as a result, these projective theories which, in part, were developed essentially during the first half of the 20th century with the works of, for instance, O. Veblen and B. Hoffmann fell almost completely into oblivion [1]. Surprisingly, the origins of such issues arised fundamentally from incomplete or strongly non-relativistic descriptions of the physical observables and localization protocols which provide direct accesses to the positions of the spacetime events. A part of the clarification appeared in the early 2000s with new designs of positioning protocols implemented in so-called ‘relativistic positioning systems’ independent of any simultaneity convention cluttering up earlier designs [2, 3, 4, 5]. However, only positions of users collecting positioning signals on their receivers can be deduced from such relativistic positioning systems. Actually, the latter do not allow any localization, i.e., they do not provide genuinely relativistic, physical observables for carrying out a system of relativistic coordinates in spacetime. The ‘relativistic localizing systems’ [6, 7] solve this remaining problem and, thereafter, the one for positioning any spacetime event.

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Dates et versions

hal-01851162 , version 1 (29-07-2018)

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Citer

Jacques L. Rubin. Consequences in fields theory and astrophysics of a projective theory of relativity emerging from relativistic localizing systems. 15th International Conference of Numerical Analysis and Applied Mathematics, Sep 2017, Thessaloniki, Greece. pp.300007, ⟨10.1063/1.5043926⟩. ⟨hal-01851162⟩
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