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Lorentz transformation (view source)
Revision as of 16:14, September 9, 2016
, 16:14, September 9, 2016More maths
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== Mathematics of the Transforms ==
=== Displacement and Time ===
The transformation from one coordinate system <math> (x, y, z, t) </math> to another system, <math> (x', y', z', t') </math>, moving past this one at speed u, and with <math>x </math> and <math> x' </math> axes colinear is:
The transformation from one coordinate system <math> (x, y, z, t) </math> to another system, <math> (x', y', z', t') </math>, moving past this one at speed u, and with <math>x </math> and <math> x' </math> axes colinear is:
where <math> \gamma </math> is the [[Lorentz factor]].
where <math> \gamma </math> is the [[Lorentz factor]].
=== Velocity Transforms ===
The velocity transforms can be found by [[derivative|differentiating]] the displacement transforms with respect to [[time]]. For the above coordinate systems, we find:
<math> v'_x = \frac{v_x -u}{1- \frac{u v_x}{c^2}} </math><br/>
<math> v'_y = \frac{v_y}{\gamma (1- \frac{u v_x}{c^2})} </math><br/>
<math> v'_z= \frac{v_z}{\gamma (1- \frac{u v_x}{c^2})} </math>
== See also ==
== See also ==
(username removed)