In 1905 Albert Einstein, with the advent of special relativity, derived the standard configuration formula ( V in the x-direction) for the addition of relativistic velocities. The aberration of light, of which the easiest explanation is the relativistic velocity addition formula, together with Fizeau's result, triggered the development of theories like Lorentz aether theory of electromagnetism in 1892. the speed is c⁄ n + (1 − 1⁄ n 2) V instead of c⁄ n + V, where c is the speed of light in the aether, n is the refractive index of the fluid, and V is the speed of the fluid with respect to the aether. 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. Fizeau experimentally correctly determined the zeroth term of an expansion of the relativistically correct addition law in terms of V⁄ c as is described below. Fizeau's results were not in accord with the then-prevalent theories.
In 1851, Fizeau measured the speed of light in a fluid moving parallel to the light using an interferometer.
The speed of light in a fluid is slower than the speed of light in vacuum, and it changes if the fluid is moving along with the light. The notation employs u as velocity of a body within a Lorentz frame S, and v as velocity of a second frame S′, as measured in S, and u′ as the transformed velocity of the body within the second frame. 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. 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. Such formulas apply to successive Lorentz transformations, so they also relate different frames.
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In relativistic physics, a velocity-addition formula is an equation that specifies how to combine the velocities of objects in a way that is consistent with the requirement that no object's speed can exceed the speed of light. The special theory of relativity, formulated in 1905 by Albert Einstein, implies that addition of velocities does not behave in accordance with simple vector addition.
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