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The "fine structure" of special relativity and the Thomas precession

par Pierseaux, Yves
Référence Annales de la fondation Louis de Broglie, 29, 1-2, page (57-118)
Publication Publié, 2004

Article révisé par les pairs

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Résumé :

The standard Special Relativity (SR) is essentially a mixture between Einstein's kinematics and Poincaré's theory of groups. The subgroup of unimodular transformations (scalar boosts) implies that Poincaré's fundamental invariant is not the four-interval but the four-volume, which defines not only the units of measure, compatible with the invariance of light speed but also an exact-scalar differential. Minkowski's four-intervall supposes a non-Euclidean definition of the space-time distance and the introduction of an non-exact differential, the element of the proper time. Poincaré's scalar boosts form a subgroup of the general group (with two space rotations). This is not the case for vector Einstein's boosts, connected with the concepts of proper time and proper system. Poincaré's two space rotations don't bring new physics whereas Thomas' space rotation, that completes Einstein's composition of vector boosts, corrects (factor 5) the value of the magnetic moment of the electron. If Poincaré's SR is completed in 1908, Thomas completed only in 1926 Einstein-Minkowski's kinematics by his correct and complete definition of the proper system (parallel transport). We show that it is not only the proper energy (Einstein), the proper mass (Planck), the proper time (Einstein-Minkowski), but also the proper magnetic moment (and also the spin 1/2) of the pointlike electron which is inscribed in Einstein- Thomas' SR, clearly separated of Poincaré's one (where the electron has a finite volume). The electron's spin 1/2 is deduced from Einstein-Thomas' group. Dirac's equation (first order with respect to the time) is invariant in Einstein's sense while the Klein-Gordon's equation (second order with respect to the time) is invariant in the sense of Poincaré. In this respect we show that Thomas' precession implies a projective and Lobatchevkian structure of the tridimensional space in Einstein-Thomas' SR, in which the electron (without structure) is never accelerated and therefore doesn't emit radiation.