Lorentz group
Matrices with , , ; general form boosts time and space coordinates.
Definition 4.34 (Lorentz Group)
The Lorentz group is the subgroup of the group above that satisfies and .
General form
Requiring , , and imposes
whose solution is
These elements compose by .
Physical interpretation of boosts
Fixing , a Lorentz transformation maps along the same branch of the hyperbola. Writing and setting , renaming and gives
a boost to an observer moving at speed . The factor produces time dilation and length contraction.
Composing velocities with gives , the relativistic velocity addition formula.
Related
Stated in
- Definition 4.34 (Lorentz Group)§4.9.2 2D Minkowski Space and Lorentz Transformations