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Article Dans Une Revue Axioms Année : 2023

The Relativistic Rotation Transformation and the Observer Manifold

Rotatation relativiste et variété des observateurs

Résumé

We show that relativistic rotation transformations represent transfer maps between the laboratory system and a local observer on an observer manifold, rather than an event manifold, in the spirit of C-equivalence. Rotation is, therefore, not a parameterised motion on a background space or spacetime, but is determined by a particular sequence of tetrads related by specific special Lorentz transformations or boosts. Because such Lorentz boosts do not form a group, these tetrads represent distinct observers that cannot put together their local descriptions into a manifold in the usual sense. The choice of observer manifold depends on the dynamical situation under consideration, and is not solely determined by the kinematics. Three examples are given: Franklin's rotation transformation for uniform plane rotation, the Thomas precession of a vector attached to an electron, and the motion of a charged particle in an electromagnetic field. In each case, at each point of its trajectory, there is a distinguished tetrad and a special Lorentz transformation that maps Minkowski space to the spacetime of the local observer on the curve.
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hal-04529372 , version 1 (02-04-2024)

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Satyanad Kichenassamy. The Relativistic Rotation Transformation and the Observer Manifold. Axioms, 2023, 12 (2), pp.205:1-16. ⟨10.3390/axioms12020205⟩. ⟨hal-04529372⟩

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