Abstract:
Weakening the Euclidean assumption in special relativity and the coordinate-independence hypothesis in general relativity for the de Sitter space, we propose a de Sitter invariant special relativity with two universal constants of speed cc and length RR based on the principle of relativity and the postulate of universal constants cc and RR on de Sitter space with Beltrami metric. We also propose a postulate on the origin of the inertial motions and inertial systems as a base of the principle of relativity. We show that the Beltrami-de Sitter space provides such a model that the origin of inertia should be determined by the cosmological constant Λ\Lambda if the length RR is linked with Λ\Lambda. In addition, via the `gnomonic' projection the uniform straight-line motion on Beltrami-de Sitter space is linked with the uniform motion along a great `circle' on de Sitter space embedded in 5-d Minkowski space.