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Encyclopedia > Velocity addition formula

A velocity addition formula appears in the special theory of relativity as a consequence of the Lorentz transformations. Different velocity addition formulae also appear in some other theories. A simple introduction to this subject is provided in Special relativity for beginners Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein. ... The Lorentz transformation (LT), named after its discoverer, the Dutch physicist and mathematician Hendrik Antoon Lorentz (1853-1928), forms the basis for the special theory of relativity, which has been introduced to remove contradictions between the theories of electromagnetism and classical mechanics. ...


Velocity addition under special relativity

Due to the time and distance distortions that must be attributed when citing measurements of a frame that is in motion relative to the observer's frame, velocities cannot be added with plain arithmetic, but must employ a more complex formula.


For special relativity, given two velocities v1, and v2,, acting colinearly, and with the same "sign" (both positive or both negative), the summation of these results in:

Where c represents the speed of light.


A feature of the formula is that no summation of velocities ever exceeds c, even if both addends should equal c.


For velocities far less than lightspeed, the formulated summation reduces to regular arithmetic addition because the second term of the denominator becomes negligible. Cherenkov effect in a swimming pool nuclear reactor. ...


Velocity-addition in other theories

Velocity addition formulae also arise outside special relativity. generally, if Shift(velocity) is defined as a frequency ratio f'/f, then we expect a theory to generate a special velocity addition formula when its Doppler relationships have the characteristic:


For emission theory, the Doppler relationship of f' / f = (cv) / c results in a velocity addition formula of Emission theory (a. ...



where VTOT is an equivalent velocity that lets us calculate the same total frequency shift in a single stage.


Although the velocity-addition formula method is general, the appearance of a v.a.f. under special relativity has a very different significance to the use of superficially-similar formulae under other theories.


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