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Velocity-addition formula
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Velocity-addition formula : ウィキペディア英語版
Velocity-addition formula
In relativistic physics, a velocity-addition formula is a equation that relates the velocities of objects in different reference frames. Such formulas apply to successive Lorentz transformations, so they also relate different frames. Accompanying velocity addition is a kinematic effect known as Thomas precession, whereby successive non-collinear Lorentz boosts become equivalent to the composition of a rotation of the coordinate system and a boost.
Standard applications of velocity-addition formulas include the Doppler shift, Doppler navigation, the aberration of light, and the dragging of light in moving water observed in the 1851 Fizeau experiment.
== History ==
The speed of light in the fluid is slower than the speed of light in vacuum, and it changes if the fluid is moving along with the light. In 1851, Fizeau measured the speed of light in a fluid moving parallel to the light using a Michelson interferometer. Fizeau's results were not in accord with the then prevalent theories. Fizeau experimentally correctly determined the zeroth term of an expansion of the relativistically correct addition law in terms of as is described below. Fizeau's result led physicists to accept the empirical validity of the rather unsatisfactory theory by Fresnel that a fluid moving with respect to the stationary aether ''partially'' drags light with it, i.e. the speed is instead of , where is the speed of light in the aether, and is the speed of the fluid with respect to the aether.
The aberration of light, which easiest explanation is the relativistic velocity addition formula, together with Fizeau's result provoked the development of theories like Lorentz aether theory of electromagnetism in 1892. It was only with the advent of special relativity in 1905 that the issues involving aether were, gradually over the years, settled.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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