Poincaré group

The Poincaré group is a fundamental set of mathematical transformations that describe the basic symmetries of space and time in Einstein's theory of special relativity. It combines rotations and boosts (changes in velocity) with translations (shifting positions in space and time). Essentially, it characterizes how the laws of physics stay consistent for observers moving at different speeds or located at different points in space-time. This group ensures that physical laws are the same regardless of how you are moving or where you are in the universe, forming the backbone of modern physics theories.