Relativistic velocity space, Wigner rotation, and Thomas precession

2004/06/14 by John A. Rhodes, Mark D. Semon · 4 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Four-momentum #General relativity #Geometry #History and Theory of Mathematics #Kinematics #Lorentz covariance #Lorentz transformation #Mathematical physics #Mathematics and Applications #Physics #Precession #Quantum mechanics #Rapidity #Relativistic particle #Relativistic speed #Relativity and Gravitational Theory #Rotation (mathematics) #Space (punctuation) #Spacetime #Special relativity #Theory of relativity #Velocity-addition formula #gr-qc #math-ph #math.MP #physics.class-ph

paper · pdf · doi:10.1119/1.1652040

published as Am.J.Phys. 72 (2004) 943 · see journal article for more information

openalex publication_date 2004/06/14 · arxiv created 2005/01/24 · arxiv updated 2015/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We develop a relativistic velocity space called rapidity space from the single assumption of Lorentz invariance, and use it to visualize and calculate effects resulting from the successive application of non-collinear Lorentz boosts. In particular, we show how rapidity space provides a geometric approach to Wigner rotation and Thomas precession in the same way that space–time provides a geometrical approach to kinematic effects in special relativity.

Citations

• On Unitary Representations of the Inhomogeneous Lorentz Group
• The Thomas precession factor in spin–orbit interaction
• Classical Electrodynamics

Cited by

• Rotation of the swing plane of Foucault's pendulum and Thomas spin precession: two sides of one coin
• Thomas Rotation and Thomas Precession
• Gyroscope precession along unbound equatorial plane orbits around a Kerr black hole
• Thomas precession [wikipedia]