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Special theory of relativity (view source)
Revision as of 16:37, September 9, 2016
, 16:37, September 9, 2016More details of mathematics
The central equations of special relativity are the [[Lorentz transformation|Lorentz transformations]]:
The central equations of special relativity are the [[Lorentz transformation|Lorentz transformations]]:
<math> x' = \gamma (x -ut) </math><br/>
<math> y' = y </math><br/>
<math> z' = z</math><br/>
<math> t' = \gamma (t - \frac{ux}{c^2} ) </math>
These are the transformations 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.
The Lorentz factor, <math>\gamma </math> occurs frequently all over special relativity and is<ref>http://www2.slac.stanford.edu/vvc/theory/relativity.html</ref>
The Lorentz factor, <math>\gamma </math> occurs frequently all over special relativity and is<ref>http://www2.slac.stanford.edu/vvc/theory/relativity.html</ref>
:<math>\gamma = \frac{1}{\sqrt{1-\frac{u^2}{c^2}}}</math>, where:
:<math>\gamma = \frac{1}{\sqrt{1-\frac{u^2}{c^2}}}</math>, where:
* <math> \gamma </math> is the Lorentz factor and relates time, mass, and momentum in different [[inertial reference frame|inertial frames of reference]].
* <math> \gamma </math> is the Lorentz factor and relates time, mass, and momentum in different [[inertial reference frame|inertial frames of reference]].
* U is the difference in speed between the frames of reference
* <math>u</math> is the difference in speed between the frames of reference
* c is the [[speed of light]]
* <math>c </math> is the [[speed of light]]
=== Classical mechanics ===
=== Classical mechanics ===
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