Difference between revisions of "Lorentz transformation"
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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: | ||
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where <math> \gamma </math> is the [[Lorentz factor]]. | where <math> \gamma </math> is the [[Lorentz factor]]. | ||
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| + | === Velocity Transforms === | ||
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| + | The velocity transforms can be found by [[derivative|differentiating]] the displacement transforms with respect to [[time]]. For the above coordinate systems, we find: | ||
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| + | <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 == | ||
Revision as of 16:14, 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]
Mathematics of the Transforms
Displacement and Time
The transformation from one coordinate system to another system, , moving past this one at speed u, and with and axes colinear is:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x' = \gamma (x -ut) }
where is the Lorentz factor.
Velocity Transforms
The velocity transforms can be found by differentiating the displacement transforms with respect to time. For the above coordinate systems, we find:
See also
References
- ↑ Michal Andrle. Whitheadova Filosofie Přírody (in Czech). Prague: Charles University, 155. ISBN 978-80-87378-22-9.