In simple and concrete terms. Suppose you observe N particles following different trajectories in Spacetime.
There are two observers traveling at constant speed relative to each other, and so they see different trajectories for those particles:
Note that the first two types of transformation are exactly the non-relativistic Galilean transformations.
- space and time shifts, because their space origin and time origin (time they consider 0, i.e. when they started their timers) are not synchronized. This can be modelled with a 4-vector addition.
- their space axes are rotated relative to one another. This can be modelled with a 4x4 matrix multiplication.
- and they are moving relative to each other, which leads to the usual spacetime interactions of special relativity. Also modelled with a 4x4 matrix multiplication.
The Poincare group is the set of all matrices such that such a relationship like this exists between two frames of reference.
- Table of contents | 192, 1k, 13
- 1. Galilean transformation | 0, 610, 5
- 2. Lorentz group () | 101, 255, 6
- Internal and spacetime symmetries | 287, 287, 2
- Lorentz group | 101, 255, 6
- Physics from Symmetry by Jakob Schwichtenberg (2015) | 118
- Lecture 1 | 257
- Spin comes naturally when adding relativity to quantum mechanics | 140, 188, 5