# 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 = (t′ + x′v/c 2)/β
β is the factor √(1 – 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.
References in periodicals archive ?
The ordinary Dirac bispinor [phi]: that transforms linearly under a Lorentz transformation i.e.
Let J be the group generated by the Lorentz transformations and the positive dilatations.
Lorentz transformation der warme und der temperatur.
Now in their 1984 work referred to above, Tzanakis and Kyritsis raised the question whether the Lorentz transformations follow from PULC, weak-PR and Einstein's remaining postulates.
Such Lorentz transformations are called parabolic since their orbits are parabolas on a given light-like plane (i.e., open curves) in contrast to the circular orbits of usual rotations.
However, Mansouri and Sexl also claim that for 1/a = b = [gamma] and [epsilon] = -v/[c.sup.2], their transformation turns into the Lorentz transformation, which is obviously wrong.
On a six-dimensional Riemannian manifold M, for example, local Lorentz transformations are orthogonal rotations in Spin(6), and spin connections [[omega].sub.AB] = [[omega].sub.MAB]d[x.sup.M] are the spin(6)-valued gauge fields from the gauge theory point of view (we will use large letters to indicate a Lie group G and small letters for its Lie algebra g).
The momentum and energy in equations (9) and (10) are derived from nothing more than the vanishing of the Lorentz transformation of (2), whose results can be taken a step further:
On the other hand, when a Lorentz transformation is performed over the physical system, this is when the experimental apparatus is rotated or boosted rather than the coordinates used to describe it, then the SM operator transforms as shown in 1) but any background field remains unchanged L' = t x O' [not equal to] L.
An important aspect of Lorentz Relativity, which causes ongoing confusion, is that the so-called Lorentz transformation is an aspect of Special Relativity, but not Lorentz Relativity.
More explicity, this gives a map of complex valued bi-spinors [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to real 4-vectors so that each 4x4 complex matrix action corresponds to a Lorentz transformation and compositions among these is preserved by this mapping.

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