Rapidity | Wikipedia audio article
Channel: wikipedia tts
Date: 08/12/2018

This is an audio version of the Wikipedia Article:
Rapidity


00:00:41 1 History
00:00:56 1.1 Area of a hyperbolic sector
00:01:05 2 In one spatial dimension
00:01:53 2.1 Exponential and logarithmic relations
00:02:03 3 In more than one spatial dimension
00:02:44 4 In experimental particle physics
00:04:02 5 See also
00:09:34 6 Remarks
00:12:06 7 Notes and references
00:19:14 undefined
00:23:44 undefined
00:24:04 undefined
00:24:13 undefined



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SUMMARY
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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 whole real line for its range, and so the interval −c  v  c maps onto −∞  w  ∞.