Special Relativity in the 21$^{\rm st}$ century

Details Special Relativity in the 21$^{\rm st}$ century Special Relativity in the 21$^{\rm st}$ century

2008-07-18

arxiv.org/abs/0807.3009v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

"to appear in the special (Sept/Oct 2008) issue of Annalen der Physik (Berlin) commemorating H. Minkowski's 1908 lecture in Co

Scientific paper

10.1002/andp.200810321

This paper, which is meant to be a tribute to Minkowski's geometrical insight, rests on the idea that the basic observed symmetries of spacetime homogeneity and of isotropy of space, which are displayed by the spacetime manifold in the limiting situation in which the effects of gravity can be neglected, leads to a formulation of special relativity based on the appearance of two universal constants: a limiting speed $c$ and a cosmological constant $\Lambda$ which measures a residual curvature of the universe, which is not ascribable to the distribution of matter-energy. That these constants should exist is an outcome of the underlying symmetries and is confirmed by experiments and observations, which furnish their actual values. Specifically, it turns out on these foundations that the kinematical group of special relativity is the de Sitter group $dS(c,\Lambda)=SO(1,4)$. On this basis, we develop at an elementary classical and, hopefully, sufficiently didactical level the main aspects of the theory of special relativity based on SO(1,4) (de Sitter relativity). As an application, we apply the formalism to an intrinsic formulation of point particle kinematics describing both inertial motion and particle collisions and decays.

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