Special relativity (alternative formulations)

About: Special relativity (alternative formulations) is a research topic. Over the lifetime, 3102 publications have been published within this topic receiving 55015 citations.

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.

Comment on: "Lorentz violation in high-energy ions" by Santosh Devasia

Abstract: In an article “Lorentz violation in high-energy ions” by S. Devasia published in this Journal [EPJ C 69, 343 (2010)], our recent Doppler shift experiments on fast ion beams are reanalyzed. Contrary to our analysis, Devasia concludes that our results provide an “indication of Lorentz violation”. We argue that this conclusion is based on a fundamental misunderstanding of our experimental scheme and reiterate that our results are in excellent agreement with Special Relativity.

Extended Lorentz Transformations in Clifford Space Relativity Theory

Abstract: Some novel physical consequences of the Extended Relativity Theory in C-spaces (Clifford spaces) were explored recently. In particular, generalized photon dispersion relations allowed for energy-dependent speeds of propagation while still retaining the Lorentz symmetry in ordinary spacetimes, but breaking the extended Lorentz symmetry in C-spaces. In this work we analyze in further detail the extended Lorentz transformations in Clifford Space and their physical implications. Based on the notion of “extended events” one finds a very different physical explanation of the phenomenon of “relativity of locality” than the one described by the Doubly Special Relativity (DSR) framework. A generalized Weyl-Heisenberg algebra, involving polyvector-valued coordinates and momenta operators, furnishes a realization of an extended Poincare algebra in C-spaces. In addition to the Planck constant ħ, one finds that the commutator of the Clifford scalar components of the Weyl-Heisenberg algebra requires the introduction of a dimensionless parameter which is expressed in terms of the ratio of two length scales : the Planck and Hubble scales. We finalize by discussing the concept of “photons”, null intervals, effective temporal variables and the addition/subtraction laws of generalized velocities in C-space.

A note on "Einstein's special relativity beyond the speed of light by James M. Hill and Barry J. Cox"

Abstract: We show that the transformations J. M. Hill and B. J. Cox introduce between inertial observers moving faster than light with respect to each other are consistent with Einstein's principle of relativity only if the spacetime is 2 dimensional.