From Pappus to Kocik’s diagram for relativistic velocity addition

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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Relativistic Velocity Addition Law from Machine Gun Analogy

The Physics Teacher ◽

10.1119/1.3049880 ◽

2009 ◽

Vol 47 (1) ◽

pp. 43-45

Author(s):

Bernhard Rothenstein ◽

Stefan Popescu

Keyword(s):

Relativistic Velocity ◽

Velocity Addition

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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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Relativistically invariant Bohmian trajectories of photons

10.21203/rs.3.rs-783149/v1 ◽

2021 ◽

Author(s):

Joshua Foo ◽

Estelle Asmodelle ◽

Austin Lund ◽

Timothy Ralph

Keyword(s):

Bohmian Mechanics ◽

Quantum Mechanical ◽

Relativistic Velocity ◽

Weak Measurements ◽

Hidden Variable ◽

Bohmian Trajectories ◽

Velocity Addition ◽

Velocity Equation ◽

Interpretation Of Quantum Theory ◽

Deterministic Trajectories

Abstract Bohmian mechanics is a nonlocal hidden-variable interpretation of quantum theory which predicts that particles follow deterministic trajectories in spacetime. Historically, the study of Bohmian trajectories has been restricted to nonrelativistic regimes due to the widely held belief that the theory is incompatible with special relativity. Here we derive expressions for the relativistic velocity and spacetime trajectories of photons in a Michelson-Sagnac-type interferometer. The trajectories satisfy quantum-mechanical continuity, the relativistic velocity addition rule. Our new velocity equation can be operationally defined in terms of weak measurements of momentum and energy. We finally propose a modified Alcubierre metric which could give rise to these trajectories within the paradigm of general relativity.

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