Symmetry Transformations in Minkowski Space

In 4 dimensions, we extend the possible symmetry transformations that we had in 3D. The laws of physics are still invariant under translations in position and in time. We still have invariance under rotations. (And we still may have parity inversions and time reversal.) Now we add invariance under Lorentz boosts.

In one sense Newton already postulated that the laws of physics were the same in any inertial frame. Einstein extended this to include the speed of light. Now this (inertial frame) invariance which seemed separate from the invariance under rotations, really is part of the same group of 4D symmetry transformations.

This set of symmetry transformations forms a group called the Lorentz Group. It includes rotations and boosts. The simplest rotations and boosts are transformations in a plane. We have just looked at the boost that is in the $xt$ plane.

If we add translation symmetries to the group, it is called the Poincare Group.

We are not using group theory here but it can be a powerful tool to understand physics.