Lorentz transformation

The [group transformation]? known as the Lorentz transformation, after physicist [H. A. Lorentz]?.

The Lorentz transformation, as a set of equations governing two [reference frame]?s in space-time, S and S', with S' traveling at a relative speed of u to S; an event has space-time coordinates of (x,y,z,t) in S and (x',y',z',t') in S':

x' = γ(x - ut)

y' = y

z' = z

t' = γ(t - uxc^-2)

where

γ = 1/√(1 - u²)

and c is the speed of light. These equations only work if u is pointed along the x-axis of S. In cases where u does not point along the x-axis of S, it is generally easier to perform a rotation so that u does point along the x-axis of S than to bother with the general case of the Lorentz transformation. Another limiting factor of the above transformation is that the "position" of the origins must coincide at 0. What this means is that (0,0,0,0) in frame S must be the same as (0,0,0,0) in S'.

Lorentz invariance

Quantities which remain the same under Lorentz transforms are said to be Lorentz invariant. The space-time interval is a [Lorentz-invariant quantity]?.

History

Lorentz discovered in 1900 that the transformation preserved Maxwell's equations. Lorentz believed the luminiferous aether hypothesis; it was Albert Einstein who developed the theory of relativity to provide a proper foundation for its application.

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