Full set of all possible special relativity symmetries:

- translations in space and time
- rotations in space
- Lorentz boosts

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.

- Important Lie groups | 0, 3k, 45
- Lie group | 278, 5k, 72
- Differential geometry | 12, 5k, 73
- Geometry | 0, 7k, 118
- Mathematics | 17, 28k, 633
- Ciro Santilli's Homepage | 262, 218k, 4k

- 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