# Lorentz transformation

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## Lorentz transformation

A set of equations used in the special theory of relativity to transform the coordinates of an event (*x*,

*y*,

*z*,

*t*) measured in one inertial frame of reference to the coordinates of the same event (

*x′*,

*y′*,

*z′*,

*t*′) measured in another frame moving relative to the first at constant velocity

*v*:

*x*= (

*x′*+

*vt′*)/β

*y*=

*y′*

z =

*z′*;t = (

β is the factor √(1 – *t′*+*x′v/c*^{2})/β*v*

^{2}/

*c*

^{2}) and

*c*is the speed of light. When

*v*is very much less than

*c*, these equations reduce to those used in classical mechanics.

Collins Dictionary of Astronomy © Market House Books Ltd, 2006

## Lorentz transformation

[′lȯr‚ens ‚tranz·fər‚mā·shən] (mathematics)

Any linear transformation of euclidean four space which preserves the quadratic form

*q(x,y,z,t)*=*t*^{2}-*x*^{2}-*y*^{2}-*z*^{2}. (relativity)

Any of the family of mathematical transformations used in the special theory of relativity to relate the space and time variables of different Lorentz frames.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

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