Boost Composition and Wigner Rotation in Rhodes-Semon Rapidity Space

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Relativistic velocity addition can be simulated by vector addition in hyperbolic space. This Demonstration shows the Rhodes–Semon construction in the Poincaré disk that computes the composition of Lorentz transformations representing noncollinear relativistic velocity additions. Use the 2D sliders

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and

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to set the combined boosts. The Wigner rotation equals the difference between the angles of the purple arrow and its parallel-transported image, the orange arrow. Alternatively, unclick the "two points" control to set the first boost

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, and then the second boost can be set as a heading angle and a rapidity with the "angle" and "rapidity" controls.