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Alfred Arthur Robb FRS [1] (18 January 1873 in Belfast – 14 December 1936 in Castlereagh) was a Northern Irish physicist. [2] Biography Robb studied at Queen's College in Belfast (BA 1894) and at St John's College in Cambridge (Tripos 1897, MA 1901)]. [3] He then proceeded to University of Göttingen, where, guided by Woldemar Voigt, he wrote his dissertation on the Zeeman effect. He also worked under J. J. Thomson at the Cavendish Laboratory. The Croix de Guerre was awarded to him for WWI service in the Red Cross, and in 1921 he became a fellow of the Royal Society. [1] [4] He is known for his four books on special relativity (1911, 1914, 1921, 1936) where he gave a spacetime derivation of the theory in an axiomatic-geometric way. [5] Robb therefore was sometimes called the "Euclid of relativity". In the first of these works he used a hyperbolic angle ω to introduce the concept of rapidity [6] : 9 and showed that the kinematic space of velocities is hyperbolic, s...

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In relativity, rapidity is commonly used as a measure for relativistic velocity. Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each frame being associated with distance and time coordinates. For one-dimensional motion, rapidities are additive whereas velocities must be combined by Einstein's velocity-addition formula. For low speeds, rapidity and velocity are proportional, but for higher velocities, rapidity takes a larger value, the rapidity of light being infinite. Using the inverse hyperbolic function artanh , the rapidity w corresponding to velocity v is w = artanh( v / c ) where c is the velocity of light. For low speeds, w is approximately v / c . Since in relativity any velocity v is constrained to the interval − c < v < c the ratio v / c satisfies −1 < v / c < 1 . The inverse hyperbolic tangent has the unit interval (−1, 1) for its domain and the w...