Lorentz transformation

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.

Related Topics:
Physicist - Mathematician - Hendrik Antoon Lorentz - 1853 - 1928 - Special theory of relativity - Electromagnetism - Classical mechanics

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Under these transformations, the speed of light is the same in all reference frames, as postulated by special relativity. Although the equations are associated with special relativity, they were developed before special relativity and were proposed by Lorentz in 1904 as a means of explaining the Michelson-Morley experiment through contraction of lengths. This is in contrast to the more intuitive Galilean transformation, which is sufficient at non-relativistic speeds (i.e. speeds much, much lower than the speed of light).

Related Topics:
Speed of light - 1904 - Michelson-Morley experiment - Galilean transformation

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It can be used (for example) to calculate how a particle trajectory looks if viewed from an inertial reference frame that is moving with constant velocity (with respect to the initial reference frame). It replaces the earlier Galilean transformation. The velocity of light, c, enters as a parameter in the Lorentz transformation. If v is low enough with respect to c then v/c o 0, and the Galilean transformation is recovered, so it may be identified as a limiting case.

Related Topics:
Inertial reference frame - Galilean transformation

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The Lorentz transformation is a group transformation that is used to transform the space and time coordinates (or in general any four-vector) of one inertial reference frame, S, into those of another one, S', with S' traveling at a relative speed of {v} to S along the x-axis. If an event has space-time coordinates of (t, x, y, z) in S and (t', x', y', z') in S', and the origins coincide (in other words (0,0,0,0) in S coincides with (0,0,0,0) in S'), then these coordinates are related according to the Lorentz transformation in the following way:

Related Topics:
Group transformation - Four-vector - Inertial reference frame - Speed - Event

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: t' = gamma left(t - rac{v x}{c^{2}} ight)

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: x' = gamma (x - v t),

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: y' = y,

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: z' = z,

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where

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: gamma equiv rac{1}{sqrt{1 - v^2/c^2}} is called the Lorentz factor and c is the speed of light in a vacuum.

Related Topics:
Lorentz factor - Speed of light

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The four equations above can be expressed together in matrix form as

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:

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egin{bmatrix}

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t' \x' \y' \z'

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end{bmatrix}

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