:t' = γ(t - ux) |
:t' = γ(t - uxc-2) |
:γ = 1/&sqrt;(1 - u2) :and units are chosen such that c= 1. |
: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'. |
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':
where