Titlebook: Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession; The Theory of Gyrogr Abraham A. Ungar Book 2001 Springer Science+Bus

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https://doi.org/10.1007/978-3-319-38939-4ion. Reading this chapter would be useful for readers who are familiar, or wish to familiarize themselves, with the standard .(2,.) formalism and its Pauli spin matrices, and who wish to see how these lead to gyrogroups and gyrovector spaces. Starting from the Pauli spin matrices and a brief descrip

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https://doi.org/10.1007/978-3-319-38939-4ay to the mainstream literature. Therefore, thirty three years later, two of them suggested considering the “notorious Thomas precession formula” (in their words, p. 431 in [RR99]) as an indicator of the quality of a formalism for dealing with the Lorentz group. The idea of Rindler and Robinson to u

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爭議的蘋果

Hyperbolic Geometry of Gyrovector Spaces,The ability of Thomas precession to unify Euclidean and hyperbolic geometry is further demonstrated in this chapter by the introduction of (i) hyperbolic rooted vectors, called rooted gyrovectors; (ii) equivalence relation between rooted gyrovectors; and (iii) translations between rooted gyrovectors, called gyrovector translations.

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The Lorentz Transformation Link,The Lorentz transformation of spacetime coordinates was developed by Lorentz [Lor95] [Lorl4] [Lor16] [Lor21] [LAH23] [Poi05] from a paper of Voigt, as confirmed by Lorentz himself [Lor21], and was efficiently applied at the early development of special relativity theory by Poincaré [Poi05].

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Gyrogeometry,n gives rise. We indicate in this chapter that gyrogeometry is the super geometry that naturally unifies Euclidean and hyperbolic geometry. The classical hyperbolic geometry of Bolyai and Lobachevski emerges in gyrogeometry with a companion, called cohyperbolic geometry.