VERY SPECIAL RELATIVITY IS INCOMPATIBLE WITH THOMAS PRECESSION

Glashow and Cohen make the interesting observation that certain proper subgroups of the Lorentz group like HOM(2) or SIM(2) can explain many results of special relativity like time dilation, relativistic velocity addition and a maximal isotropic speed of light. We show here that such SIM(2) and HOM(2) based VSR theories predict an incorrect value for the Thomas precession and are therefore ruled out by observations. In VSR theories the spin-orbital coupling in atoms turn out to be too large by a factor of 2. The Thomas–BMT equation derived from VSR predicts a precession of electrons and muons in storage rings which is too large by a factor of 103. VSR theories are therefore ruled out by observations.

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Thomas precession and spin interaction energy in very special relativity

Modern Physics Letters A ◽

10.1142/s0217732314501405 ◽

2014 ◽

Vol 29 (26) ◽

pp. 1450140

Author(s):

Hassan Ganjitabar ◽

Ali Shojai

Keyword(s):

Special Relativity ◽

Interaction Energy ◽

Electromagnetic Fields ◽

Spin Interaction ◽

Poincaré Group ◽

Thomas Precession ◽

Poincare Group ◽

External Electromagnetic Fields ◽

Very Special Relativity

Very Special Relativity (VSR), proposed by Cohen and Glashow, considers one of the subgroups of Poincaré group as the symmetry of spacetime. This paper investigates the transformations of electromagnetic fields under boosts of VSR, and by the aid of them studies the interaction energy between spin of an electron and external electromagnetic fields. Here, we argue that Thomas precession, one of the consequences of Special Relativity (SR), does not exist in HOM(2) avatar of VSR. The predictions of SR and VSR about the spin interaction energy in a certain case are compared, and despite the absence of Thomas precession in VSR, no noticeable departure is seen.

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Relativistic velocity addition from the geometry of momentum space

European Journal of Physics ◽

10.1088/1361-6404/ac41d7 ◽

2021 ◽

Author(s):

Angel Paredes Galan ◽

Xabier Prado ◽

Jorge Mira

Keyword(s):

Special Relativity ◽

Momentum Space ◽

Mass Shell ◽

Relativistic Velocity ◽

Visual Tool ◽

Momentum Plane ◽

Velocity Addition ◽

Graphical Illustration

Abstract With the goal of developing didactic tools, we consider the geometrization of the addition of velocities in special relativity by using Minkowski diagrams in momentum space. For the case of collinear velocities, we describe two ruler-and-compass constructions that provide simple graphical solutions working with the mass-shell hyperbola in a 1+1-dimensional energy-momentum plane. In the spirit of dimensional scaffolding, we use those results to build a generalization in 1+2 dimensions for the case of non-collinear velocities, providing in particular a graphical illustration of how the velocity transverse to a boost changes while the momentum remains fixed. We supplement the discussion with a number of interactive applets that implement the diagrammatic constructions and constitute a visual tool that should be useful for students to improve their understanding of the subtleties of special relativity.

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Special Relativity: Putting it All Together

10.1093/oso/9780199658633.003.0008 ◽

2018 ◽

Author(s):

David M. Wittman

Keyword(s):

Special Relativity ◽

Moving Object ◽

Velocity Addition

We have introduced the ideas of special relativity in quick succession because none of those ideas can really be understood in isolation. This chapter works through examples in some detail so you can practice applying the ideas and solidifying your understanding.We start with an overview of how to use spacetime diagrams to solve problems in special relativity, then we walk through examples ofmeasuring the length of a moving object; the train‐in‐tunnel paradox; velocity addition; and how clock readings are arranged so that each observer measures the other’s clocks as ticking slowly.

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