Galilean transform
Assuming the relative motion 'v' is along the x dimension then x'=x-vt so the transform will be:
|
= |
| 1 |
0 |
0 |
0 |
| -v |
1 |
0 |
0 |
| 0 |
0 |
1 |
0 |
| 0 |
0 |
0 |
1 |
|
|
Lorentz transform
The Lorentz transform relates the spacetime coordinates (t,x,y,z) to (t',x',y',z'), spacetime in different frames.
Assuming the relative motion 'v' is along the x dimension then the transform will be:
|
= |
 |
-b |
0 |
0 |
| -b |
|
0 |
0 |
| 0 |
0 |
1 |
0 |
| 0 |
0 |
0 |
1 |
|
|
where:
- = 1/sqrt(1 - ß2)
- b = ß/sqrt(1 - ß2)
- ß = v/c
- v = relative velocity
- c = speed of light
If the velocity is not along the 'x' dimension then we can rotate in the3 space dimensions, apply the simple Lorentz transform, then apply the reverse space rotation.
Any 4x4 matrix (or corresponding linear transformation) that preserves the quadratic form xt G x is called Lorentz.
