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

TL;DR

This paper revisits special relativity by incorporating a cosmological constant, leading to a de Sitter group framework that extends the classical theory and offers new insights into particle kinematics.

Contribution

It introduces a formulation of special relativity based on the de Sitter group SO(1,4), incorporating a cosmological constant into the spacetime symmetry structure.

Findings

The kinematical group of special relativity is the de Sitter group SO(1,4).

The formalism provides an intrinsic description of particle motion and interactions.

Confirms the existence and experimental validation of the constants c and Λ.

Abstract

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.