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

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.

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

References in corpus (22)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Dynamics of dark energy
• On cosmic acceleration without dark energy
• Sakharov's induced gravity: a modern perspective
• Cosmic clocks, cosmic variance and cosmic averages
• Exact solution to the averaging problem in cosmology
• Analyticity properties and thermal effects for general quantum field theory on de Sitter space-time
• de Sitter special relativity
• Lifetime of a massive particle in a de Sitter universe
• On Special Relativity with Cosmological Constant
• On Beltrami Model of de Sitter Spacetime
• Gravitational energy as dark energy: Concordance of cosmological tests
• Elie Cartan's torsion in geometry and in field theory, an essay
• On Principle of Inertia in Closed Universe
• On covariant long-distance modifications of Einstein theory and strong coupling problem
• Conservation laws and scattering for de Sitter classical particles
• Algebraic and geometric structures of Special Relativity
• Lectures on Inflationary Cosmology
• Vacuum energy and spectral function sum rules
• Cosmological Term and Fundamental Physics

Cited by in corpus (25)

• Symmetries of quantum space-time in 3 dimensions
• Doubly special relativity in de Sitter spacetime
• Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime
• Kinematics of particles with quantum de Sitter symmetries
• Foundations of anisotropic relativistic mechanics
• Gauge Theory of Gravity with de Sitter Symmetry as a Solution to the Cosmological Constant Problem and the Dark Energy Puzzle
• Deformed General Relativity and Torsion
• Qualitative study of perfect-fluid Friedmann-Lema\^ıtre-Robertson-Walker models with a cosmological constant
• On the spacetime connecting two aeons in conformal cyclic cosmology
• de Sitter geodesics: reappraising the notion of motion
• Noncommutative Yang model and its generalizations
• An Invariant Approach to Weyl's unified field theory
• de Sitter geodesics
• $\kappa$-de Sitter and $\kappa$-Poincaré symmetries emerging from Chern-Simons (2+1)D gravity with a cosmological constant
• de Sitter relativity in central charts
• Linear Canonical Transformations in Relativistic Quantum Physics
• "Nonrelativistic" kinematics: Particles or waves?
• Dual DSR
• de Sitter invariant special relativity and galaxy rotation curves
• de Sitter-invariant special relativity and the dark energy problem
• Entropy in locally-de Sitter spacetimes
• On Geometry and Symmetries in Classical and Quantum Theories of Gauge Gravity
• de Sitter geodesics in stereographic charts
• Collective classical motion on hyperbolic spacetimes of any dimensions
• Conserved quantities for the Sitter particles${}^{\ast }$