On de Sitter Invariant Special Relativity and Cosmological Constant as Origin of Inertia

Details On de Sitter Invariant Special Relativity and Cosmological Constant as Origin of Inertia On de Sitter Invariant Special Relativity and Cosmological Constant as Origin of Inertia

2004-05-15

arxiv.org/abs/hep-th/0405137v3

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, revtex4

Scientific paper

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 $c$ and length $R$ based on the principle of relativity and the postulate of universal constants $c$ and $R$ 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 $\Lambda$ if the length $R$ is linked with $\Lambda$. 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.

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