Difference between revisions of "Lorentz transformation"
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'''Lorentz transformations''' form the group of linear isometries of [[Minkowski space]]. | '''Lorentz transformations''' form the group of linear isometries of [[Minkowski space]]. | ||
| − | In [[physics]], a Lorentz transformation is the conversion of space and time between two different [[Inertial reference frame|inertial frames of reference]]. | + | In [[physics]], a Lorentz transformation is the conversion of space and time between two different [[Inertial reference frame|inertial frames of reference]]. |
According to [[Einstein]] the principles of [[Special Relativity]] are mathematically expressed by Lorentz transformations owing to which it is possible to transform equations for mechanical and electromechanical phenomena between inertial systems.<ref>{{cite book | According to [[Einstein]] the principles of [[Special Relativity]] are mathematically expressed by Lorentz transformations owing to which it is possible to transform equations for mechanical and electromechanical phenomena between inertial systems.<ref>{{cite book | ||
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|pages=155 | |pages=155 | ||
|quote= | |quote= | ||
| − | |language=Czech}}</ref> | + | |language=Czech}}</ref> |
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| + | 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: | ||
| + | |||
| + | <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> | ||
| + | |||
| + | where <math> \gamma </math> is the [[Lorentz factor]]. | ||
== See also == | == See also == | ||
Revision as of 15:55, September 9, 2016
Lorentz transformations form the group of linear isometries of Minkowski space.
In physics, a Lorentz transformation is the conversion of space and time between two different inertial frames of reference.
According to Einstein the principles of Special Relativity are mathematically expressed by Lorentz transformations owing to which it is possible to transform equations for mechanical and electromechanical phenomena between inertial systems.[1]
The transformation from one coordinate system to another system, , moving past this one at speed u, and with and axes colinear is:
where is the Lorentz factor.
See also
References
- ↑ Michal Andrle. Whitheadova Filosofie Přírody (in Czech). Prague: Charles University, 155. ISBN 978-80-87378-22-9.