Showing papers on "Special relativity (alternative formulations) published in 1971"

Galilei Group and Galilean Invariance

Abstract: Publisher Summary Galileo Galilei explicitly introduced the principle of relativity in physics. He was the first one to recognize the existence of inertial transformations, connecting various frames of reference in which the laws of physics take the same form. Starting with the recognition that the Galilean transformation laws were but an approximation to the more exact Lorentz formulas, one could distinguish the abstract principle of relativity from its concrete expressions, as various possible theories of relativity. At the same time, one could begin to see the basic role played by the relevant theory of relativity in structuring a given physical theory—Galilean relativity for classical mechanics, Einstein relativity for “relativistic” mechanics, and electromagnetism. Applications of the Galilei group are described for classical physics and for quantum physics. A “super-Galilei group” has been defined in relation to non-relativistic cosmology. This is a sixteen-parameter group acting on the five-dimensional manifold of space-time and gravitational potential.

Magnetized deformable media in general relativity

Abstract: In this article, we develop from a variational formulation the field equations, jump conditions across a discontinuity surface and nonlinear constitutive equations for a magnetized elastic medium with finite deformations in the frame of the general theory of relativity. RESUME. Dans le present article, nous généralisons dans le cadre de la relativité générale, la théorie des milieux continus déformables en interaction avec le champ magnétique donnée precedemment dans le cadre de la relativité restreinte [6][25]-[27]. Le milieu continu considéré est un milieu solide élastique sujet a des deformations finies et en interaction avec les champs gravifique et magnétique. Un principe variationnel qui suit la formulation que Taub [12] a donnée pour le schema fluide parfait est employe. Toutes les equations du champ (equations d’Einstein, conservation de 1’impulsion-energie, equations de Maxwell dans un milieu matériel, conservation du flux d’entropie) en découlent ainsi que les conditions de saut a travers une surface de discontinuité. Comme dans le travail de Taub, il est montré que cette derniere ne peut etre variée indépendamment du parametre thermodynamique. Les lois non-linéaires de comportement sont également obtenues a partir d’un potentiel, l’énergie libre de Helmholtz qui est écrite sous forme invariante, ceci généralisant la contrainte habituellement imposée par le principe d’indifference matérielle en mécanique classique des milieux continus. ANN. INST. POINCARÉ, A-X V-4 20 276 G~RARD A. MAUGIN

The social roots of Einstein's theory of relativity

Abstract: (1971). The social roots of Einstein's theory of relativity. Annals of Science: Vol. 27, No. 4, pp. 313-344.

Spinor fields in general relativity: II: Generalized field equations and application to the dirac field

Abstract: SummaryThis is the continuation of the previous paper. The action function of matter is supplemented by the action function of a free field. With the help of the usual variational formalism we derive the field equations, which show the correspondence between the canonical energy momentum and Einstein’s tensor as well as the correspondence between the canonical spin angular momentum and contorsion. It is shown that these equations are consistent with the conservation laws as derived in the previous paper. As a simple example we consider the Dirac field in this formalism. We show that spin angular momentum in this case is completely antisymmetric and that the additional terms in the action function arising from torsion express a spin-spin contact interaction. The generalized Dirac equation is shown to be equivalent to a nonlinear spinor equation of Heisenberg-Pauli type in which the nonlinear term is induced by torsion.RiassuntoQuesto è il seguito dell’articolo precedente. La funzione di azione della materia è completata con la funzione di azione di un campo libero. Con l’aiuto dell’usuale formalismo Tariazionale si deducono le equazioni di campo che mostrano la corrispondenza fra l’energia-impulso canonica ed il tensore di Einstein ed anche la corrispondenza fra il momento angolare di spin canonico e la contorsione. Si mostra che queste equazioni sono consistenti con le leggi di conservazione dedotte nell’articolo precedente. Come semplice esempio si considera in questo formalismo il campo di Dirac. Si dimostra che in questo caso il momento angolare dello spin è completamente antisimmetrico e che i termini addizionali nella funzione di azione derivanti dalla torsione esprimono un’interazione di contattp spin-spin. Si dimostra che l’equazione di Dirae generalizzata è equivalente ad un’equazione spinoriale non lineare del tipo di Heisenberg-Pauli in cui il termine non lineare è introdotto dalla torsione.РезюмеЭта работа представляет продолжение предыдущей статьи. Функция действия вещества дополняется функцией действия свободного поля. С помощью обычного вариационного формализма мы выводим уравнения поля, которые обнаруживают соответствие между каноническим тензором энергии-импульса и тензором Эйнштейна, а также соответствие между каноническим спиново-орбитальным моментом и искажением. Показывается, что эти уравнения не противоречат законам сохранения, выведенным в предыдущей статье. В качестве примера мы рассматриваем поле Дирака в этом формализме. Мы показываем, что спиново-орбитальный момент в этом случае является полностью антисимметричным, и дополнительные члены в функции действия, возникающие из закручивания, выражают спин-спиновое контактное взаимодействие. Показывается, что обобщенное уравнение Дирака эквивалентно нелинейному спинорному уравнению типа Гайзенберга-Паули, в котором нелинейный член обусловлен закручиванием.

On the Advance of the Perihelion According to Special Relativity

Abstract: Undergraduate classes of physics and applied mathematics, in their studies of introductory relativity theory, are often presented with a special-relativistic calculation of the perihelion advance of planetary orbits. The result comes to be one-sixth of the gen-eral-relativistic value and serves as a demonstration of the inability of special relativity to account for the residual effect observed in the case of Mercury. As well, the calculation provides a rather pleasant example (perhaps more from the teacher’s viewpoint than the student’s) of two-dimensional relativistic particle dynamics.