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.

Contributions of K. Gödel to relativity and cosmology

Abstract: K Gδdel published two seminal papers on general relativity theory and its application to the study of cosmology. The first examined a non-expanding but rotating solution of the Einstein field equations, in which causality is violated; this lead to an in-depth examination of the concepts of causality and time in curved space-times. The second examined properties of a family of rotating and expanding spatially homogeneous solutions of the Einstein equations, which was a forerunner of many studies of such cosmologies. Together they stimulated examination of themes that were fundamental in the development of the Hawking-Penrose singularity theorems and in studies of cosmological dynamics. I review these two papers, and the developments that resulted from them.

Some Remarks on the Infinite De Sitter Space

Abstract: One can define de Sitter space as a four-dimensional space with the following two properties. First, it is invariant under the operations of a transitive ten-parametric group. Four of the infinitesimal operators of this group are usually made to correspond to the components of the energy-momentum vector, the other six to the angular momentum tensor. Second, the subgroup of this ten-parametric group which leaves a given point of the space invariant must be isomorphic to the ordinary homogeneous Lorentz group. This last point ensures that the neighborhood of any point of these de Sitter spaces behaves like the flat space of special relativity (Minkowski space).

Simple Derivation of Minimum Length, Minimum Dipole Moment and Lack of Space–Time Continuity

Abstract: The principle of maximum power makes it possible to summarize special relativity, quantum theory and general relativity in one fundamental limit principle each. Special relativity contains an upper limit to speed; following Bohr, quantum theory is based on a lower limit to action; recently, a maximum power given by c 5/4G was shown to be equivalent to the full field equations of general relativity. Taken together, these three fundamental principles imply a limit value for every physical observable, from acceleration to size. The new, precise limit values differ from the usual Planck values by numerical prefactors of order unity. Among others, minimum length and time intervals appear. The limits imply that elementary particles are not point-like and suggest a lower limit on electric dipole values. The minimum intervals also imply that the non-continuity of space–time is an inevitable result of the unification of quantum theory and relativity, independently of the approach used.

Special Relativity as a non commutative geometry: Lessons for Deformed Special Relativity

Abstract: Deformed Special Relativity (DSR) is obtained by imposing a maximal energy to Special Relativity and deforming the Lorentz symmetry (more exactly the Poincar\'e symmetry) to accommodate this requirement. One can apply the same procedure deforming the Galilean symmetry in order to impose a maximal speed (the speed of light). This leads to a non-commutative space structure, to the expected deformations of composition of speed and conservation of energy-momentum. In doing so, one runs into most of the ambiguities that one stumbles onto in the DSR context. However, this time, Special Relativity is there to tell us what is the underlying physics, in such a way that we can understand and interpret these ambiguities. We use these insights to comment on the physics of DSR.