Lorentz transformations form the group of linear isometries of Minkowski space.
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.
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:
Note how the transformations for velocity in the y and z directions also depend on the velocity of the particle in the x direction, not just the relative speed between the frames of reference. This is different to the displacement transformations, in which y and z are independent of x.
- Michal Andrle. Whitheadova Filosofie Přírody (in Czech). Prague: Charles University, 155. ISBN 978-80-87378-22-9.
- Bradley W. Carroll, Dale A Ostlie. An Introduction to Modern Astrophysics (in English). London: Pearson.